Problem of the Week

Updated at Jul 25, 2016 3:36 PM

For this week we've brought you this calculus problem.

How can we find the derivative of x6+cot⁡x{x}^{6}+\cot{x}?

Here are the steps:



ddxx6+cot⁡x\frac{d}{dx} {x}^{6}+\cot{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)).
(ddxx6)+(ddxcot⁡x)(\frac{d}{dx} {x}^{6})+(\frac{d}{dx} \cot{x})

2
Use Power Rule: ddxxn=nxn−1\frac{d}{dx} {x}^{n}=n{x}^{n-1}.
6x5+(ddxcot⁡x)6{x}^{5}+(\frac{d}{dx} \cot{x})

3
Use Trigonometric Differentiation: the derivative of cot⁡x\cot{x} is −csc⁡2x-\csc^{2}x.
6x5−csc⁡2x6{x}^{5}-\csc^{2}x

Done
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