# Problem of the Week

## Updated at Jan 8, 2018 4:38 PM

This week we have another calculus problem:

How can we solve for the derivative of $${x}^{4}\tan{x}$$?

Let's start!

$\frac{d}{dx} {x}^{4}\tan{x}$

 1 Use Product Rule to find the derivative of $${x}^{4}\tan{x}$$. The product rule states that $$(fg)'=f'g+fg'$$.$(\frac{d}{dx} {x}^{4})\tan{x}+{x}^{4}(\frac{d}{dx} \tan{x})$2 Use Power Rule: $$\frac{d}{dx} {x}^{n}=n{x}^{n-1}$$.$4{x}^{3}\tan{x}+{x}^{4}(\frac{d}{dx} \tan{x})$3 Use Trigonometric Differentiation: the derivative of $$\tan{x}$$ is $$\sec^{2}x$$.$4{x}^{3}\tan{x}+{x}^{4}\sec^{2}x$Done4*x^3*tan(x)+x^4*sec(x)^2