# Und3rstanding

Back to calculus...

$$ln(f(x))'=\frac{f'(x)}{f(x)}$$

why, why, why?

Note by Aloysius Ng
3 years, 7 months ago

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By chain rule: $\ln(f(x))'=\frac{d}{dx}\ln x{\Huge|}_{x=f(x)}\times f'(x)=\frac1x{\Huge|}_{x=f(x)}\times f'(x)=\frac{f'(x)}{f(x)}$

- 3 years, 7 months ago

Let f(x)=u. By the chain rule, d/dx (ln(f(x)= 1/u times u'=1/f(x) times f'(x). So, that's the basic proof :)

- 3 years, 7 months ago