Problem of the Week

Updated at Jul 12, 2021 10:27 AM

How can we find the derivative of \(8u+\ln{u}\)?

Below is the solution.



\[\frac{d}{du} 8u+\ln{u}\]

1
Use Sum Rule: \(\frac{d}{dx} f(x)+g(x)=(\frac{d}{dx} f(x))+(\frac{d}{dx} g(x))\).
\[(\frac{d}{du} 8u)+(\frac{d}{du} \ln{u})\]

2
Use Power Rule: \(\frac{d}{dx} {x}^{n}=n{x}^{n-1}\).
\[8+(\frac{d}{du} \ln{u})\]

3
The derivative of \(\ln{x}\) is \(\frac{1}{x}\).
\[8+\frac{1}{u}\]

Done
Cymath foriOSAndroid