Problem of the Week

Updated at Jul 18, 2016 11:37 AM

How would you differentiate cos⁡x−x9\cos{x}-{x}^{9}?

Below is the solution.



ddxcos⁡x−x9\frac{d}{dx} \cos{x}-{x}^{9}

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)).
(ddxcos⁡x)+(ddx−x9)(\frac{d}{dx} \cos{x})+(\frac{d}{dx} -{x}^{9})

2
Use Trigonometric Differentiation: the derivative of cos⁡x\cos{x} is −sin⁡x-\sin{x}.
−sin⁡x+(ddx−x9)-\sin{x}+(\frac{d}{dx} -{x}^{9})

3
Use Power Rule: ddxxn=nxn−1\frac{d}{dx} {x}^{n}=n{x}^{n-1}.
−sin⁡x−9x8-\sin{x}-9{x}^{8}

Done
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