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Homework Statement
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.
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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