Problem of the Week

Updated at Apr 17, 2017 2:13 PM

This week we have another calculus problem:

How would you differentiate \({e}^{x}-x\)?

Let's start!



\[\frac{d}{dx} {e}^{x}-x\]

1
Use Sum Rule: \(\frac{d}{dx} f(x)+g(x)=(\frac{d}{dx} f(x))+(\frac{d}{dx} g(x))\).
\[(\frac{d}{dx} {e}^{x})+(\frac{d}{dx} -x)\]

2
The derivative of \({e}^{x}\) is \({e}^{x}\).
\[{e}^{x}+(\frac{d}{dx} -x)\]

3
Use Power Rule: \(\frac{d}{dx} {x}^{n}=n{x}^{n-1}\).
\[{e}^{x}-1\]

Done
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