Problem of the Week

Updated at Sep 1, 2014 8:36 AM

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

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

Here are the steps:



ddxx6+cos⁡x\frac{d}{dx} {x}^{6}+\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)).
(ddxx6)+(ddxcos⁡x)(\frac{d}{dx} {x}^{6})+(\frac{d}{dx} \cos{x})

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

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

Done
Cymath foriOSAndroid