# Problem of the Week

## Updated at Dec 12, 2016 11:06 AM

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: $$\frac{d}{dx} {x}^{n}=n{x}^{n-1}$$.$\ln{({x}^{4})}+4$Doneln(x^4)+4