1)Derivar:
![{\displaystyle F'(x)=4x^{3}-14x}](https://wikimedia.org/api/rest_v1/media/math/render/svg/bb6e8e6e860e4d8d596e3c6da6939e3194bfc7ad)
--Corredorclau 14:08, 12 Jul 2004 (UTC)
2)Derivar:
![{\displaystyle F'(x)=10x-2}](https://wikimedia.org/api/rest_v1/media/math/render/svg/cdf06ae760ddd07649813f8a26e9ca85864ddb78)
--Corredorclau 14:15, 12 Jul 2004 (UTC)
3)Derivar:
![{\displaystyle F'(x)=2(2x^{2}-5)(4x)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5fce32043094956d3946e5d47721bf69670158e3)
![{\displaystyle F'(x)=(4x^{2}-10)(4x)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/44f0eee5899300726e068bb8c8d9d0e42548712f)
![{\displaystyle F'(x)=16x^{3}-40~~~by:corredorclau}](https://wikimedia.org/api/rest_v1/media/math/render/svg/eae8c119ab5fcbe80c90969b735f480d6ba1da8d)
Los siguientes ejercicios fueron tomados del libro de Howard E. Taylor.
4)Derivar:
![{\displaystyle f'(x)={\frac {x-3}{x^{2}}}+{\frac {x^{2}-(2x)(7)}{x^{4}}}+3x^{-4}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7b818f1aee00a35675e0e84053075e3b51a9926d)
![{\displaystyle f'(x)={\frac {-3}{x^{2}}}-{\frac {14x}{(x^{4}}}+3x^{-4}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/81e90d2e55a4cbc706479d87d074dd9a8b318277)
![{\displaystyle f'(x)={\frac {-3}{x^{2}}}-{\frac {14}{(x^{3}}}+{\frac {3}{x^{4}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3ccc77f3e7ea469514b0f90a7742078a93e9e95c)
Corredorclau 18:18, 13 Jul 2004 (UTC)
5)Derivar:
![{\displaystyle F'(x)={\frac {1}{3}}+3x^{{\frac {1}{3}}-1}+7cosx}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7e8054da540a3eebd244ba3430a0177661b89a72)
![{\displaystyle F'(x)=3x^{\frac {-2}{3}}+7cosx}](https://wikimedia.org/api/rest_v1/media/math/render/svg/369f7e795072b4b28c2dfd18cd08cc232c21a1bf)
Corredorclau
6)Derivar:
![{\displaystyle F'(x)={\sqrt {5+x^{2}}}+x\cdot {\frac {1}{2{\sqrt {5+x^{2}}}}}\cdot 2x}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3bfd00effda9b71c912f598fbfe46be490173546)
![{\displaystyle F'(x)={\sqrt {5+x^{2}}}+{\frac {2x^{2}}{2{\sqrt {5+x^{2}}}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7529f8358980616da41efd63afc9c6f88cf5d0a7)
![{\displaystyle F'(x)={\frac {{\sqrt {5+x^{2}}}+x^{2}}{\sqrt {5+x^{2}}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/06dabde390a3e9276753ad4261d4e2cda873422a)
![{\displaystyle F'(x)={\frac {5+x^{2}+x^{2}}{\sqrt {5+x^{2}}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8b0ca8d216a070b1d16441fd3952ee974de72b91)
![{\displaystyle F'(x)={\frac {5+2x^{2}}{\sqrt {5+x^{2}}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/bd544a87792c711db0e14156740a3a84766852a3)
Corredorclau
7)Derivar:
![{\displaystyle \ 6x+8yy'=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2c819e75ed925a3816759a37ce7c8ca0948796bc)
![{\displaystyle \ 8yy'=6x}](https://wikimedia.org/api/rest_v1/media/math/render/svg/133d99008843eb88176afbe9d1e02b5bee16d7b2)
![{\displaystyle \ y'={\frac {6x}{8y}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ae76f30085b9883a2a2aa165cef2d6bcbba6e68f)
![{\displaystyle \ y'={\frac {-3x}{4y}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3a663a1c31efe392a60b317fb6375f6b505d8528)
Corredorclau 21:44, 13 Jul 2004 (UTC)
8)Derivar:
![{\displaystyle \ F'(x)=(2x)(x^{4}+5)+(x^{5}-4)(4x^{3})}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4ebaa134295636553374b9d39c2780612aeddd09)
![{\displaystyle \ F'(x)=2x^{5}+10x+4x^{5}-16x^{3}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b6a854b0f0996290a8b29df03fb5c2f8622f4ffd)
![{\displaystyle \ F'(x)=6x^{5}-16x^{3}+10x}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8fb5ee5dd247f0b57649b27d2623918efc00ce57)
Corredorclau 12:48, 13 Jul 2004 (UTC)
9)Derivar:
![{\displaystyle \ F'(x)=4x(2x-4)+2x^{2}(2)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/32f6a3e5922fb26a4daee89a1c4aee1e5595c646)
![{\displaystyle \ F'(x)=8x^{2}-16x+4x^{2}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6de32651f9d56a3cb21392791df61f33d5210626)
![{\displaystyle \ F'(x)=12x2-16x}](https://wikimedia.org/api/rest_v1/media/math/render/svg/df211b7d0fff2d1c16828a3d4d743ca87842630b)
Corredorclau 12:48, 13 Jul 2004 (UTC)
10)Derivar:
![{\displaystyle \ y'(x)=9x^{2}-8x+5+0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/313be52834d4f2c69b56f0d1cb6b4e5b9a3239e8)
![{\displaystyle \ y'(x)=9x^{2}-8x+5}](https://wikimedia.org/api/rest_v1/media/math/render/svg/cf067c5139b3bb81fcd6ac07b826c2803af3606d)
JORGE MARIO MEDINA MARTIN 5:10, 13 Jul 2004
11):
![{\displaystyle f'(x)={\frac {cosx(x)-senx}{x^{2}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e30bdd7be8f7e2daa265f2aa7d9f8d6c3134e7cb)
![{\displaystyle f'(x)={\frac {cosx}{x}}-{\frac {senx}{x^{2}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a5b4055a16b72e36e2e6df52d725d11d40a9a07c)
Corredorclau
12)Derivar:
![{\displaystyle f'(x)={\frac {(6X^{2}-4(3senx))-(2x^{3}-4x)3cosx}{(3senx)^{2}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c0e89e94c39e8ce232eacc77be0a97ab391266eb)
![{\displaystyle f'(x)={\frac {18x^{2}senx-12senx-6x^{3}cosx+12xcosx}{9sen^{2}x}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a03db84369a2c0a62e691641c4e567f2cee62f4c)
Corredorclau
13)Derivar:
![{\displaystyle f'(x)={\frac {2(x^{2}-2x)(2x-2)}{(x^{2}-2x)^{4}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e106397e1da03a1abf1d0dd8b3c1c0d9b1a59245)
![{\displaystyle f'(x)={\frac {4x-4}{(x^{2}-2x)^{3}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/348aaf34ca2805d8c21aa4fc986dfbb3b98974ec)
Corredorclau
14)Derivar:
![{\displaystyle f'(x)={\frac {-cosx(1+cosx)-(1-senx)-senx}{1+cosx}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0ce380bf7d68e94ac35a99cf827b84c84fc6187f)
![{\displaystyle f'(x)={\frac {-cosx-cos^{2}x+senx-sen^{2}x}{1+cos^{2}x}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d7a84b5eecf157ec59da25871291e371c4218054)
![{\displaystyle f'(x)={\frac {-cosx-1+sen^{2}x+senx-sen^{2}x}{(1+cosx)^{2}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/dd357c953a8c354f22a869ee3f18fa76f8399f86)
![{\displaystyle f'(x)={\frac {-cosx-1+senx}{(1+cosx)^{2}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/df548356f1fb4237f6851e06324f25991c6daf5b)
Corredorclau
15)Derivar:
![{\displaystyle f'(x)={\frac {2(cos2x)sen2x(2)(x^{2})-2x(cos^{2}2x)}{x^{4}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/260d5d342193547f8e64a6caeed9e44cc9590d50)
![{\displaystyle f'(x)={\frac {4senx-2x}{x^{2}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ba4cb52bd8569afa29d13bc5414a67555357c41d)
Corredorclau
16)Derivar:
![{\displaystyle f'(x)={\frac {-7senx}{49}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1eeaa5bfddd3fdebcdf880ecaa0e1143dc371e8b)
![{\displaystyle f'(x)={\frac {-senx}{7}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d964e12e3a80b0e9c66c609adae3fe4c79f4bee6)
Corredorclau
17)Derivar:
![{\displaystyle f'(x)={\frac {2(x-1)(x^{2})-(x-1)^{2}2x}{x^{4}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5cefc842b979a27b8620e9635dbf1f36d36fefc3)
![{\displaystyle f'(x)={\frac {(2x-2)(x^{2})-(x^{2}-2x+1)2x}{x^{4}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/27bd0cfc8ae29855061cbb3aa3fbe37b6252c306)
![{\displaystyle f'(x)={\frac {2x^{3}-^{2}x^{2}-2x^{3}+4x^{2}-2x}{x^{4}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7579b1edc1627fd5e11a20493c50993971247602)
![{\displaystyle f'(x)={\frac {2x^{2}-2x}{x^{4}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/87ef0d5b7b1aef0756f092ff632bd91d47ccf285)
![{\displaystyle f'(x)={\frac {2x(x-1)}{x^{4}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c5d69959be024c65b5ca5e957db4eaf8c7233ae0)
![{\displaystyle f'(x)={\frac {2(x-1)}{x^{3}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7aa844af11392e6b021bdcb36cac7e6e35184dd6)
Corredorclau
18)Derivar:
![{\displaystyle f(x)=2(x+{\frac {1}{x}})(1-{\frac {-1}{x^{2}}})}](https://wikimedia.org/api/rest_v1/media/math/render/svg/92bd370a4bba8546f051ca730d3035efcf2a6095)
![{\displaystyle f(x)=(2x+{\frac {2}{x}})(1-({\frac {1}{x^{2}}})}](https://wikimedia.org/api/rest_v1/media/math/render/svg/205a219196e92f08301cb90bd92830e5f0e2f7f7)
![{\displaystyle f(x)=({\frac {2x^{2}+2}{x}})({\frac {x^{2}-1}{x^{2}}})}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8cdcc418dd47afd6ce8439fe595e149fbd49c5a1)
![{\displaystyle f(x)={\frac {2x^{2}-2x^{2}+2x^{2}-2}{x^{3}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5eaf63a4edae964f9b6e15a8540ecbff6dc3ec30)
![{\displaystyle f(x)={\frac {2x^{4}-2}{x^{3}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f1f6d1292caf4472e0b9354fd47da7b12f13f758)
Corredorclau
19)derivar:
![{\displaystyle f'(x)=5cos^{4}(2x^{3}+4)(6x^{2})}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6468ee294271b10dfde21f690236b983e118c958)
![{\displaystyle f'(x)=30x^{2}cos^{4}(2x^{3}+4)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1e5a01e97ea26971b5e46e98d01d62e352f0e38a)
Corredorclau
20)derivar:
![{\displaystyle f'(x)=cos7x(7)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/74a59b12ddacdd617e3186d8ba41af2cd36ceb41)
![{\displaystyle f'(x)=7cox7x}](https://wikimedia.org/api/rest_v1/media/math/render/svg/cbad59b11f738d19e79d112a5c4bf089fe169d20)
Corredorclau
21)derivar y calcular f'(1):
![{\displaystyle f'(t)=cos(t^{2}+3t+1)(2t+3)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1ed16cfbfa2dcba85fa35a160abf51ae86bab646)
![{\displaystyle f'(1)=cos25}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ad14a1eae376ff664ed6d4590743d1a3e73d0bce)
Corredorclau
22) derivar y hallar g'(1):
![{\displaystyle g'(t)=3(t^{2}+9)(2t)(t^{2}-2)^{4}+(t^{2}+9)^{3}(4)(t^{2}-2)^{3}(2t)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e0c26d8d21547e3b52e6761ad99936e37b02f85d)
![{\displaystyle g'(t)=(3t^{2}+27)^{2}(2t^{3}-4t)^{4}+(t^{2}+9)^{3}(4)(t^{2}-2)^{3}(2t)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5efb23e4205d7676a4506bc7ccb87c3d3fd37f9b)
![{\displaystyle g'(1)=-113600}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2746298afee7f227915105be50b10b77fa986be4)
Corredorclau
23)encontrar la recta tangente de
![{\displaystyle y=(x^{2}+1)^{3}(x^{4}+1)^{2}enlospuntos(1,32)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e6869a4218533f53e546e6dc2fdf2af7426c1422)
![{\displaystyle y'=3(x^{2}+1)(2x)(x^{4}+1)^{2}+(x^{2}+1)^{3}2(x^{4}+1)(4x^{3})}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0310e5f36938f27acffeebab4fa6f7f2e3127ac4)
![{\displaystyle evaluoax=1eny'}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f33953d2d695140c05efdb1eed8e8f8ae711c8fb)
![{\displaystyle 224}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e205d6871fcea516b0bffadb628b6f6e6afb846f)
![{\displaystyle laecuaciondelarectaesy=224x-192}](https://wikimedia.org/api/rest_v1/media/math/render/svg/cda68b1b039c4bfb9f5002abc2a43d2a73085109)
Corredorclau
24) derivar:
![{\displaystyle f'(x)=10x+4+{\frac {35x^{4}}{x^{1}0}}-8senx}](https://wikimedia.org/api/rest_v1/media/math/render/svg/70604bf6a122aa31d6c841fe0822bdb8c7c1e9a1)
![{\displaystyle f'(x)=10x+4+{\frac {35}{x^{6}}}-8senx}](https://wikimedia.org/api/rest_v1/media/math/render/svg/aad0ce710d5bc65d0b2ff05c7a6ac47d9ca2df38)
Corredorclau
25)halle la segunda derivada de:
![{\displaystyle f'(x)=senx+xcosx}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f5170073987785d3bb581a35cc3fb430cac8aaf9)
![{\displaystyle f''(x)=cosx+cosx-xsenx}](https://wikimedia.org/api/rest_v1/media/math/render/svg/503d15c720419906acf0c909cbcdfe753cd1385c)
![{\displaystyle f''(x)=2cosx-xsenx}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ca2f88adb8e5d9d4afa8fb5cc3bbd4d93738054f)
Corredorclau
26)halle la segunda derivada de
![{\displaystyle f'(x)=15(1+x)^{1}4}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b7af5f5ef9d34fb051a05895543375166bdb8441)
![{\displaystyle f''(x)=210(1+x)^{1}3}](https://wikimedia.org/api/rest_v1/media/math/render/svg/384415cff55d757b11e3d06f5695677231b09cb2)
Corredorclau
27):
![{\displaystyle f'(x)=5(7+x)^{4}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e6896e40ea1edf207bc331e65dbbbe299741e30e)
![{\displaystyle f''(x)=2087+x)^{3}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/84a692205e70db0bed249995ad218abf67a19a8c)
Corredorclau
28):
![{\displaystyle f'(x)=5(3-2x)^{4}(-2)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0433d154bbb7212fa96c12b64f05b305ae2c8b49)
![{\displaystyle f'(x)=-10(3-2x)^{4}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9b9a434e7e38d036a961a5f63c16433e7ac2b7fc)
![{\displaystyle f''(x)=-40(3-2x)^{3}(-2)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1f41fb3791b0c59ed9260b6c2c2240d270658143)
![{\displaystyle f''(x)=80(3-2x)^{3}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/463ab4a408efe9278b05f6501a78083d39f13352)
Corredorclau
29):
![{\displaystyle f'(x)=7(4+2x^{2})^{6}(4x)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2368a715a558fecf658e9cd495be26a19d115d94)
![{\displaystyle f'(x)=28x(4+2x^{2})^{6}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e7833f8230a8a41d2c2f83c3010813886457343f)
![{\displaystyle f''(x)=28(4+2x^{2})^{6}+28x(4+2x^{2})^{5}(4x)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/58a7fa4017b9f59644150bc83c3ec7aec8a5bc04)
![{\displaystyle f''(x)=12(4+2x^{2})^{6}+112x^{2}(4+2x^{2})^{5}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d7414a1aba0f8e05c45c9bbc04b26795ca3b6f6c)
Corredorclau
30):
![{\displaystyle 6X+8YY'=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/780a64528bd796510fb0389b8dd6d74bdb4101f8)
![{\displaystyle 8YY'=-6X}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ae3027473dd3c1f31d23b73afafb5bd9b35bc24b)
![{\displaystyle Y'={\frac {6x}{8y}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d77f570048fa7d61912b4178925fa2cf77254753)
Corredorclau
31):
![{\displaystyle 3x^{2}+3y^{2}y'-6x+6x+6yy'=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/17927086e07005401c9c67f2eb3eb222b5a5919e)
![{\displaystyle 3y^{2}y'+6yy'=-3x^{2}+6x}](https://wikimedia.org/api/rest_v1/media/math/render/svg/67e3a197ff0dd37d51d878119eb3e1086b43c365)
![{\displaystyle y'(3y^{2}+6y)=-3x^{2}+6x}](https://wikimedia.org/api/rest_v1/media/math/render/svg/817a07839d75e30bd96e978b57d1d24933e6e062)
![{\displaystyle y'=-{\frac {3x^{2}+6y}{3y^{2}+6y}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e4242970dccf94ce64055e8dea8548e83d0d8f8e)
Corredorclau
32):
![{\displaystyle cosx-senyy'=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2bee05f5873a7ce30355ccc5b85897993e77ebea)
![{\displaystyle -senyy'=-cosx}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d8b125f2bec40d5c1b8dd3bd0db4b472b33546b1)
![{\displaystyle y'={\frac {cosx}{seny}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f8024e1ce17c7de0757eb2e05a193d6bce2a779a)
Corredorclau
33):
![{\displaystyle 12x^{2}+7y^{2}+7x2yy'=6y^{2}y'}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1edfeb53b04209c27db430339e90a75badaa54f6)
![{\displaystyle 12x^{2}+7y^{2}=6y^{2}y'-7x2yy'}](https://wikimedia.org/api/rest_v1/media/math/render/svg/283baccc39c3d1943c4a0097b430ebddf078ba6d)
![{\displaystyle 12x^{2}+7y^{2}=y'(6y^{2}-7x2y)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/409b03a10d089c26e47b00992ba04fc74212de73)
![{\displaystyle {\frac {12x^{2}+7y^{2}}{6y^{2}-7x2y}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1fc0d47c312324e5573c089da38f5ed3c6f64cf8)
Corredorclau
Es utilizada para derivar funciones compuestas,primero se deriva la compuesta y se multiplica por la interna.
34):
![{\displaystyle f'(t)=3({\frac {3t-2}{t+5}})^{2}({\frac {3(t+5)-(3t-2)}{(t+5)^{2}}})}](https://wikimedia.org/api/rest_v1/media/math/render/svg/781b1f56de0fb987985639598797f740b84e4e02)
![{\displaystyle f'(t)=3({\frac {3t-2}{t+5}})^{2}({\frac {17}{(t+5)^{2})}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/32d6d8af723f337184f515538de0610093488e6a)
Corredorclau
35):
![{\displaystyle f'(t)={\frac {3(3t-2)^{2}3(t+5)-(3t-2)^{3}}{(t+5)^{2}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/511b6bd691492b8f282791170ec6f32fb52b8ac3)
![{\displaystyle f'(t)={\frac {6t+30(3t-2)^{2}-(3t-2)^{3}}{(t+5)^{2}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c7a2ae6a65496fa147f4592f73e4641044392897)
Corredorclau
36):
![{\displaystyle f'(x)=3cosx^{2}(cos)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/60191a1015bfac04121f2435ae9375d37eb3bc20)
Corredorclau
37):
- Failed to parse (syntax error): {\displaystyle f´(t)=(costtan(t^2+1)+sentsec^2(t^2+1)(2t))}
![{\displaystyle f'(t)=(costtan(t^{2}+1)+sentsec^{2}(2t^{3}+2t))}](https://wikimedia.org/api/rest_v1/media/math/render/svg/383045569e47bd7afade7bdb22217e323f977a4d)
Corredorclau
38):
![{\displaystyle H'(x)={\frac {1}{2{\sqrt {x^{2}-1}}}}(2x)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8a4b8a0cbd9b915d0db9478b19de15d7133634ce)
![{\displaystyle H'(x)={\frac {x}{\sqrt {x^{2}-1}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c12322d5df3bd3cff5446b29185ee775812f791b)
Corredorclau
39):
![{\displaystyle 2senxcosx+cosx^{2}(2x)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b9f3c22d62714af00791a6394363557cdd1dd3c5)
Corredorclau
1) Al lado de un gran muro de una granja. se quiere cercar un terreno que tenga forma rectangular. Se dispone solamente de 100 metros de malla de alambre para construir la cerca para que esta encierre la mayor parte de área posible.
![{\displaystyle A=xy}](https://wikimedia.org/api/rest_v1/media/math/render/svg/52ff5da8e68347fd1c8cece0aa71e418f93a66ef)
![{\displaystyle 2x+y=100}](https://wikimedia.org/api/rest_v1/media/math/render/svg/94ccf1cd006c9c17bf2815d06e2d7620193043e6)
![{\displaystyle y=100-2x}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7dd90d2b53388e0140207fc5c4dfeb1cc7b02086)
![{\displaystyle A=x(100+2x)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/dc0389f83a44c55657c6644bb805e82a169e1713)
![{\displaystyle A=100x-2x^{2}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1b53e03b21193897eb8beed20a9a4481c88157d5)
![{\displaystyle A'=100-4x}](https://wikimedia.org/api/rest_v1/media/math/render/svg/03de058c80d60773acd96cde8a6281570c52e8b9)
![{\displaystyle A'=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/60da124645459b50387fcad3461fddb3e448619d)
![{\displaystyle 100-4x=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ea70ab15421d215cac376e3e34057de3cc1dec9c)
![{\displaystyle -4x=-100}](https://wikimedia.org/api/rest_v1/media/math/render/svg/116af823848772452635dce0393bdd72e7944e16)
![{\displaystyle x={\frac {100}{4}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/dc4efbf3bff50a391df0590701d1a23e759d979e)
![{\displaystyle x=25}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0bbe492fdf59c36d880068344239762c8fd62451)
![{\displaystyle y=100-2x}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7dd90d2b53388e0140207fc5c4dfeb1cc7b02086)
![{\displaystyle y=100-50}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6b93e2d8fcd724356f763ba2c9d19695a2658f74)
![{\displaystyle y=25}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7a744f29298ee7906d0534e40001796be3846a58)
![{\displaystyle A=xy}](https://wikimedia.org/api/rest_v1/media/math/render/svg/52ff5da8e68347fd1c8cece0aa71e418f93a66ef)
![{\displaystyle A=25(50)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3d30da50bec9cc3483bdeba83b3dc1a06858f8d6)
![{\displaystyle A=1250metros}](https://wikimedia.org/api/rest_v1/media/math/render/svg/940c4228b16e445025cf2daa71f0fa8a41f95267)
Corredorclau
2) cual es la maxima area que puede tener un triangulo rectangulo cuya hipotenusa tenga 5cm de largo.
Por pitagoras
![{\displaystyle Z^{2}=x^{2}+y^{2}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ead351991b80c43fcc52054e501f337406931894)
![{\displaystyle z=5}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e5b5dbfc85ad671af1ec625575be8e9ba1fb9ec5)
![{\displaystyle x^{2}+y^{2}=25}](https://wikimedia.org/api/rest_v1/media/math/render/svg/918951e8e7e900ca20e45513737f11296377aed5)
![{\displaystyle y={\sqrt {25-x^{2}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c950382f902ba32ce6e157bad47b8e3de74e705b)
area del triangulo
![{\displaystyle A={\frac {xy}{2}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/710d1fe6bbb814e9d4361044d3593a55bbba5c33)
![{\displaystyle A=x({\frac {\sqrt {25-x^{2}}}{2}})}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9a8467a1e055178c878c9243ecbdf392cefbc22d)
![{\displaystyle {\frac {1}{2}}{\sqrt {25-x^{2}}}+({\frac {(}{x}}{2})({\frac {-2x}{2({\sqrt {25-x^{2}}})}}=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/53d80361325ceb74923392de0f51bc359318e4aa)
![{\displaystyle {\frac {25-x^{2}-x^{2}}{2{\sqrt {25-x^{2}}}}}=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/39fc4ce7b60f7b0d313e837a1039f18adcf0c6d9)
![{\displaystyle 25-2x^{2}=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d77e3f79ad40ecef4b4ecb1348c8b76f90505ac2)
![{\displaystyle x={\sqrt {\frac {25}{2}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e6295b2369230e1b22e9f7e92be8341196ee0587)
![{\displaystyle y={\sqrt {25-{\frac {25}{2}}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3c0d407bf2177317ad2aee60ee80c84bd29f52fd)
![{\displaystyle y={\sqrt {\frac {25}{2}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/170cf6fc354a50d60cc00cc494635d32d976b64b)
![{\displaystyle A={\frac {\sqrt {\frac {25}{2}}}{\sqrt {\frac {25}{2}}}}{2}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/41f54a19aa977d5be782e98d9b179127aa089e8c)
![{\displaystyle A={\frac {25}{4}}cm^{2}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0914a8941821026b755bb7091472011cee013983)
Corredorclau