Problem of the Week

Updated at Jul 21, 2025 11:25 AM

This week's problem comes from the calculus category.

How would you differentiate \(\ln{v}+{v}^{2}\)?

Let's begin!



\[\frac{d}{dv} \ln{v}+{v}^{2}\]

1
Use Sum Rule: \(\frac{d}{dx} f(x)+g(x)=(\frac{d}{dx} f(x))+(\frac{d}{dx} g(x))\).
\[(\frac{d}{dv} \ln{v})+(\frac{d}{dv} {v}^{2})\]

2
The derivative of \(\ln{x}\) is \(\frac{1}{x}\).
\[\frac{1}{v}+(\frac{d}{dv} {v}^{2})\]

3
Use Power Rule: \(\frac{d}{dx} {x}^{n}=n{x}^{n-1}\).
\[\frac{1}{v}+2v\]

Done
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