A-level Mathematics/Edexcel/Core 1/Differentiation

Differentiation is the opposite to integration and you use dy/dx. To differentiate an equation, you drop the power in the front of the equation and you decrease the power by 1.

E.g. $y=3x^{2}+4x^{5}$ becomes

${\frac {dy}{dx}}=6x^{1}+20x^{4}$ or ${\frac {dy}{dx}}=6x+20x^{4}$

By substituting x values into dy/dx, you are able to find the gradient at a certain point on a graph.

${\frac {dy}{dx}}$ is known as the first deriative of an equation. ${\frac {dy}{dx}}$ is known as the second deriative. It is first deriative differentiated a second time.

Continuing from the example above,

${\frac {dy}{dx}}=6x+20x^{4}$ becomes

${\frac {d^{2}y}{dx^{2}}}=6+80x^{3}$

The deriatives can be displayed in a few different ways in questions. It can be presented as dy/dx or f'(x).