Problem of the Week

Updated at Apr 26, 2021 11:30 AM

This week's problem comes from the calculus category.

How can we find the derivative of x3+ln⁡x{x}^{3}+\ln{x}?

Let's begin!



ddxx3+ln⁡x\frac{d}{dx} {x}^{3}+\ln{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)).
(ddxx3)+(ddxln⁡x)(\frac{d}{dx} {x}^{3})+(\frac{d}{dx} \ln{x})

2
Use Power Rule: ddxxn=nxn−1\frac{d}{dx} {x}^{n}=n{x}^{n-1}.
3x2+(ddxln⁡x)3{x}^{2}+(\frac{d}{dx} \ln{x})

3
The derivative of ln⁡x\ln{x} is 1x\frac{1}{x}.
3x2+1x3{x}^{2}+\frac{1}{x}

Done
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