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 \({x}^{3}+\ln{x}\)?

Let's begin!



\[\frac{d}{dx} {x}^{3}+\ln{x}\]

1
Use Sum Rule: \(\frac{d}{dx} f(x)+g(x)=(\frac{d}{dx} f(x))+(\frac{d}{dx} g(x))\).
\[(\frac{d}{dx} {x}^{3})+(\frac{d}{dx} \ln{x})\]

2
Use Power Rule: \(\frac{d}{dx} {x}^{n}=n{x}^{n-1}\).
\[3{x}^{2}+(\frac{d}{dx} \ln{x})\]

3
The derivative of \(\ln{x}\) is \(\frac{1}{x}\).
\[3{x}^{2}+\frac{1}{x}\]

Done
Cymath foriOSAndroid