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

1 Answer
Alan N.
Aug 4, 2016

#f'(x) = 5#

Explanation:

#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#

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