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

Theorem (Computational laws for logarithmic derivatives)

For two differentiable functions ${\displaystyle f}$ and ${\displaystyle g}$ without zeros there is

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