Problem of the Week

Updated at Feb 24, 2020 3:23 PM

This week we have another calculus problem:

How can we solve for the derivative of en+7n{e}^{n}+7n?

Let's start!



ddnen+7n\frac{d}{dn} {e}^{n}+7n

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)).
(ddnen)+(ddn7n)(\frac{d}{dn} {e}^{n})+(\frac{d}{dn} 7n)

2
The derivative of ex{e}^{x} is ex{e}^{x}.
en+(ddn7n){e}^{n}+(\frac{d}{dn} 7n)

3
Use Power Rule: ddxxn=nxn−1\frac{d}{dx} {x}^{n}=n{x}^{n-1}.
en+7{e}^{n}+7

Done
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