Problem of the Week

Updated at Apr 25, 2016 8:53 AM

This week we have another calculus problem:

How can we solve for the derivative of ex−x{e}^{x}-x?

Let's start!



ddxex−x\frac{d}{dx} {e}^{x}-x

1
Use Sum Rule: ddxf(x)+g(x)=(ddxf(x))+(ddxg(x))\frac{d}{dx} f(x)+g(x)=(\frac{d}{dx} f(x))+(\frac{d}{dx} g(x)).
(ddxex)+(ddx−x)(\frac{d}{dx} {e}^{x})+(\frac{d}{dx} -x)

2
The derivative of ex{e}^{x} is ex{e}^{x}.
ex+(ddx−x){e}^{x}+(\frac{d}{dx} -x)

3
Use Power Rule: ddxxn=nxn−1\frac{d}{dx} {x}^{n}=n{x}^{n-1}.
ex−1{e}^{x}-1

Done
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