Problem of the Week

Updated at Feb 27, 2017 4:32 PM

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

Below is the solution.



ddxtan⁡x+cos⁡x\frac{d}{dx} \tan{x}+\cos{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)).
(ddxtan⁡x)+(ddxcos⁡x)(\frac{d}{dx} \tan{x})+(\frac{d}{dx} \cos{x})

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

3
Use Trigonometric Differentiation: the derivative of cos⁡x\cos{x} is −sin⁡x-\sin{x}.
sec⁡2x−sin⁡x\sec^{2}x-\sin{x}

Done
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