Exercises: Derivatives 1 – "Math for Non-Geeks"

Computation rules for derivatives

Proof of computational laws

Theorem (Computational laws for logarithmic derivatives)

For two differentiable functions $f$ and $g$ without zeros there is

1. $L({\sqrt[{k}]{f}})={\tfrac {1}{k}}L(f)$ for $k\in \mathbb {N}$ and $f>0$
2. $L(f^{\alpha })=\alpha L(f)$ for $\alpha \in \mathbb {R}$ and $f>0$
3. $L(f+g)=L(f)+L(1+{\tfrac {f}{g}})$