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**The problem statement, all variables and given/known data**

Differentiate [itex]x=e^{-x}[/itex]

**The attempt at a solution**

[tex]\ln{x}=\ln{e^{-x}}[/tex]

[tex]\ln{x}=-x[/tex]

[tex]\frac{d}{dx}\left(\ln{x}\right)=\frac{d}{dx}\left(-x\right)[/tex]

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

The correct answer is [itex]1+e^{-x}[/itex]. I know how to solve it that way; however, why is the above method wrong? I know there are usually two variables, but I can't see any mathematical errors in my method.

Thank you.

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