Problem of the Week

Updated at Aug 17, 2020 4:16 PM

For this week we've brought you this calculus problem.

How would you differentiate \({v}^{5}+\sec{v}\)?

Here are the steps:



\[\frac{d}{dv} {v}^{5}+\sec{v}\]

1
Use Sum Rule: \(\frac{d}{dx} f(x)+g(x)=(\frac{d}{dx} f(x))+(\frac{d}{dx} g(x))\).
\[(\frac{d}{dv} {v}^{5})+(\frac{d}{dv} \sec{v})\]

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

3
Use Trigonometric Differentiation: the derivative of \(\sec{x}\) is \(\sec{x}\tan{x}\).
\[5{v}^{4}+\sec{v}\tan{v}\]

Done
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