Problem of the Week

Updated at Jul 9, 2018 3:02 PM

How can we solve for the derivative of tan⁡x+x8\tan{x}+{x}^{8}?

Below is the solution.



ddxtan⁡x+x8\frac{d}{dx} \tan{x}+{x}^{8}

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)).
(ddxtan⁡x)+(ddxx8)(\frac{d}{dx} \tan{x})+(\frac{d}{dx} {x}^{8})

2
Use Trigonometric Differentiation: the derivative of tan⁡x\tan{x} is sec⁡2x\sec^{2}x.
sec⁡2x+(ddxx8)\sec^{2}x+(\frac{d}{dx} {x}^{8})

3
Use Power Rule: ddxxn=nxn−1\frac{d}{dx} {x}^{n}=n{x}^{n-1}.
sec⁡2x+8x7\sec^{2}x+8{x}^{7}

Done
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