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 n5+en{n}^{5}+{e}^{n}?

Let's start!



ddnn5+en\frac{d}{dn} {n}^{5}+{e}^{n}

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)).
(ddnn5)+(ddnen)(\frac{d}{dn} {n}^{5})+(\frac{d}{dn} {e}^{n})

2
Use Power Rule: ddxxn=nxn−1\frac{d}{dx} {x}^{n}=n{x}^{n-1}.
5n4+(ddnen)5{n}^{4}+(\frac{d}{dn} {e}^{n})

3
The derivative of ex{e}^{x} is ex{e}^{x}.
5n4+en5{n}^{4}+{e}^{n}

Done
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