Problem of the Week:
Derivative of \({e}^{x}-x\)

Updated at Apr 17, 2017 2:13 PM

This week we have another calculus problem:

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

Let's start!



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

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

Done