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Und3rstanding

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

why, why, why?

Note by Aloysius Ng
2 years, 6 months ago

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By chain rule: \[\ln(f(x))'=\frac{d}{dx}\ln x{\Huge|}_{x=f(x)}\times f'(x)=\frac1x{\Huge|}_{x=f(x)}\times f'(x)=\frac{f'(x)}{f(x)}\] Little Baby · 2 years, 6 months ago

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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 :) Abhijeet Vats · 2 years, 6 months ago

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