Problem of the Week

Updated at Sep 25, 2017 8:20 AM

This week's problem comes from the calculus category.

How can we solve for the derivative of \({x}^{2}+\tan{x}\)?

Let's begin!



\[\frac{d}{dx} {x}^{2}+\tan{x}\]

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

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

3
Use Trigonometric Differentiation: the derivative of \(\tan{x}\) is \(\sec^{2}x\).
\[2x+\sec^{2}x\]

Done
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