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)`

``

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)`

``