What is the derivative of $ln (e^{5 x})$ $ln(e^(5x))$ ?

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Answer 1 · 2016-08-04T00:20:00

$f'(x) = 5$

$f(x) = ln(e^(5x)) = 5x$ (By definition of $ln$ )

$f'(x) = 5$ (Power rule)

NB: This result can also be obtained by using the standard differential of $ln(x)$ and the chain rule as follows:

$f'(x) = 1/e^(5x) * e^(5x) * 5$
$f'(x) = 1/cancel(e^(5x)) * cancel(e^(5x)) * 5$
$f'(x)=5$

What is the derivative of ln(e^(5x))ln(e5x)ln(e^(5x))?