Question

Differentiate the following function: Y= ln(e^x +xe^x)

Answer 1

\[\frac{d}{dx}[\ln(f(x))]=\frac{f'(x)}{f(x)}\]

Answer 2

in your case \(f(x)=e^x+xe^x\) and so
\[f'(x)=e^x+e^x+xe^x=2e^x+xe^x\]

Answer 3

you good from there?

Answer 4

Yeah I have the answer thanks!

Answer 5

\[\frac{1}{x+1}+1 \]Refer to the Mathematica attachment.