Problem of the Week

Updated at Jan 31, 2022 10:53 AM

This week we have another calculus problem:

How can we solve for the derivative of \({n}^{5}+{e}^{n}\)?

Let's start!



\[\frac{d}{dn} {n}^{5}+{e}^{n}\]

1
Use Sum Rule: \(\frac{d}{dx} f(x)+g(x)=(\frac{d}{dx} f(x))+(\frac{d}{dx} g(x))\).
\[(\frac{d}{dn} {n}^{5})+(\frac{d}{dn} {e}^{n})\]

2
Use Power Rule: \(\frac{d}{dx} {x}^{n}=n{x}^{n-1}\).
\[5{n}^{4}+(\frac{d}{dn} {e}^{n})\]

3
The derivative of \({e}^{x}\) is \({e}^{x}\).
\[5{n}^{4}+{e}^{n}\]

Done
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