Problem of the Week

Updated at Nov 6, 2017 4:48 PM

This week we have another calculus problem:

How can we find the derivative of sin⁡x+tan⁡x\sin{x}+\tan{x}?

Let's start!



ddxsin⁡x+tan⁡x\frac{d}{dx} \sin{x}+\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)).
(ddxsin⁡x)+(ddxtan⁡x)(\frac{d}{dx} \sin{x})+(\frac{d}{dx} \tan{x})

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

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

Done
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