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 \(\tan{y}+{y}^{7}\)?

Here are the steps:



\[\frac{d}{dy} \tan{y}+{y}^{7}\]

1
Use Sum Rule: \(\frac{d}{dx} f(x)+g(x)=(\frac{d}{dx} f(x))+(\frac{d}{dx} g(x))\).
\[(\frac{d}{dy} \tan{y})+(\frac{d}{dy} {y}^{7})\]

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

3
Use Power Rule: \(\frac{d}{dx} {x}^{n}=n{x}^{n-1}\).
\[\sec^{2}y+7{y}^{6}\]

Done
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