Problem of the Week

Updated at Feb 23, 2015 1:13 PM

This week we have another calculus problem:

How would you differentiate \({x}^{7}-{e}^{x}\)?

Let's start!



\[\frac{d}{dx} {x}^{7}-{e}^{x}\]

1
Use Sum Rule: \(\frac{d}{dx} f(x)+g(x)=(\frac{d}{dx} f(x))+(\frac{d}{dx} g(x))\).
\[(\frac{d}{dx} {x}^{7})-(\frac{d}{dx} {e}^{x})\]

2
Use Power Rule: \(\frac{d}{dx} {x}^{n}=n{x}^{n-1}\).
\[7{x}^{6}-(\frac{d}{dx} {e}^{x})\]

3
The derivative of \({e}^{x}\) is \({e}^{x}\).
\[7{x}^{6}-{e}^{x}\]

Done
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