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 v5+sec⁡v{v}^{5}+\sec{v}?

Here are the steps:



ddvv5+sec⁡v\frac{d}{dv} {v}^{5}+\sec{v}

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)).
(ddvv5)+(ddvsec⁡v)(\frac{d}{dv} {v}^{5})+(\frac{d}{dv} \sec{v})

2
Use Power Rule: ddxxn=nxn−1\frac{d}{dx} {x}^{n}=n{x}^{n-1}.
5v4+(ddvsec⁡v)5{v}^{4}+(\frac{d}{dv} \sec{v})

3
Use Trigonometric Differentiation: the derivative of sec⁡x\sec{x} is sec⁡xtan⁡x\sec{x}\tan{x}.
5v4+sec⁡vtan⁡v5{v}^{4}+\sec{v}\tan{v}

Done
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