Problem of the Week

Updated at Dec 14, 2015 8:00 AM

This week's problem comes from the calculus category.

How can we find the derivative of sin⁡x+x4\sin{x}+{x}^{4}?

Let's begin!



ddxsin⁡x+x4\frac{d}{dx} \sin{x}+{x}^{4}

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)+(ddxx4)(\frac{d}{dx} \sin{x})+(\frac{d}{dx} {x}^{4})

2
Use Trigonometric Differentiation: the derivative of sin⁡x\sin{x} is cos⁡x\cos{x}.
cos⁡x+(ddxx4)\cos{x}+(\frac{d}{dx} {x}^{4})

3
Use Power Rule: ddxxn=nxn−1\frac{d}{dx} {x}^{n}=n{x}^{n-1}.
cos⁡x+4x3\cos{x}+4{x}^{3}

Done
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