Problem of the Week

Updated at Apr 4, 2016 3:25 PM

This week's problem comes from the calculus category.

How would you differentiate x7−sin⁡x{x}^{7}-\sin{x}?

Let's begin!



ddxx7−sin⁡x\frac{d}{dx} {x}^{7}-\sin{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)).
(ddxx7)−(ddxsin⁡x)(\frac{d}{dx} {x}^{7})-(\frac{d}{dx} \sin{x})

2
Use Power Rule: ddxxn=nxn−1\frac{d}{dx} {x}^{n}=n{x}^{n-1}.
7x6−(ddxsin⁡x)7{x}^{6}-(\frac{d}{dx} \sin{x})

3
Use Trigonometric Differentiation: the derivative of sin⁡x\sin{x} is cos⁡x\cos{x}.
7x6−cos⁡x7{x}^{6}-\cos{x}

Done
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