`f(x) = log_5 (xe^x)` Differentiate the function.

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Chapter 3, 3.6 - Problem 8 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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mathace | (Level 3) Assistant Educator

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Given: `f(x)=log_(5)(xe^x)`

`f'(x)=(1)/((xe^x)ln5)(xe^x+e^x(1))`

`f'(x)=(e^x(x+1))/((xe^x)(ln5))`

`f'(x)=(x+1)/(xln5)` 

The derivative is: `f'(x)=(x+1)/(xln5)`

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