Problem of the Week

Updated at Aug 29, 2022 11:16 AM

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

How would you differentiate tan⁡y+y7\tan{y}+{y}^{7}?

Here are the steps:



ddytan⁡y+y7\frac{d}{dy} \tan{y}+{y}^{7}

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)).
(ddytan⁡y)+(ddyy7)(\frac{d}{dy} \tan{y})+(\frac{d}{dy} {y}^{7})

2
Use Trigonometric Differentiation: the derivative of tan⁡x\tan{x} is sec⁡2x\sec^{2}x.
sec⁡2y+(ddyy7)\sec^{2}y+(\frac{d}{dy} {y}^{7})

3
Use Power Rule: ddxxn=nxn−1\frac{d}{dx} {x}^{n}=n{x}^{n-1}.
sec⁡2y+7y6\sec^{2}y+7{y}^{6}

Done
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