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 x2+tan⁡x{x}^{2}+\tan{x}?

Let's begin!



ddxx2+tan⁡x\frac{d}{dx} {x}^{2}+\tan{x}

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)).
(ddxx2)+(ddxtan⁡x)(\frac{d}{dx} {x}^{2})+(\frac{d}{dx} \tan{x})

2
Use Power Rule: ddxxn=nxn−1\frac{d}{dx} {x}^{n}=n{x}^{n-1}.
2x+(ddxtan⁡x)2x+(\frac{d}{dx} \tan{x})

3
Use Trigonometric Differentiation: the derivative of tan⁡x\tan{x} is sec⁡2x\sec^{2}x.
2x+sec⁡2x2x+\sec^{2}x

Done
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