Problem of the Week

Updated at Nov 2, 2015 4:06 PM

For this week we've brought you this calculus problem.

How can we find the derivative of \(x\ln{({x}^{4})}\)?

Here are the steps:



\[\frac{d}{dx} x\ln{({x}^{4})}\]

1
Use Product Rule to find the derivative of \(x\ln{({x}^{4})}\). The product rule states that \((fg)'=f'g+fg'\).
\[(\frac{d}{dx} x)\ln{({x}^{4})}+x(\frac{d}{dx} \ln{({x}^{4})})\]

2
Use Power Rule: \(\frac{d}{dx} {x}^{n}=n{x}^{n-1}\).
\[\ln{({x}^{4})}+x(\frac{d}{dx} \ln{({x}^{4})})\]

3
Use Chain Rule on \(\frac{d}{dx} \ln{({x}^{4})}\). Let \(u={x}^{4}\). The derivative of \(\ln{u}\) is \(\frac{1}{u}\).
\[\ln{({x}^{4})}+\frac{x(\frac{d}{dx} {x}^{4})}{{x}^{4}}\]

4
Use Power Rule: \(\frac{d}{dx} {x}^{n}=n{x}^{n-1}\).
\[\ln{({x}^{4})}+4\]

Done
Cymath foriOSAndroid