(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Differentiate

[tex]y=\ln(e^{-x} + xe^{-x})[/tex]

2. Relevant equations

- Logarithmic differentiation?

3. The attempt at a solution

Here goes:

[tex]y=\ln(e^{-x} + xe^{-x})[/tex]

[tex]y'=\frac{e^{-x} + (x\frac{d}{dx}e^{-x}+e^{-x}\frac{d}{dx}x)}{e^{-x}+xe^{-x}})[/tex]

[tex]\frac{e^{-x}+xe^{-x}+e^{-x}}{e^{-x}+xe^{-x}}[/tex]

I must be missing something huge here because the book's solution is

[tex]y'=\frac{-x}{1+x}[/tex]

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# Homework Help: Differentiate y=\ln(e^{-x} + xe^{-x})

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