# Problem of the Week

## Updated at Jan 15, 2018 3:50 PM

This week's problem comes from the calculus category.

How can we solve for the derivative of $$7x\tan{x}$$?

Let's begin!

$\frac{d}{dx} 7x\tan{x}$

 1 Use Constant Factor Rule: $$\frac{d}{dx} cf(x)=c(\frac{d}{dx} f(x))$$.$7(\frac{d}{dx} x\tan{x})$2 Use Product Rule to find the derivative of $$x\tan{x}$$. The product rule states that $$(fg)'=f'g+fg'$$.$7((\frac{d}{dx} x)\tan{x}+x(\frac{d}{dx} \tan{x}))$3 Use Power Rule: $$\frac{d}{dx} {x}^{n}=n{x}^{n-1}$$.$7(\tan{x}+x(\frac{d}{dx} \tan{x}))$4 Use Trigonometric Differentiation: the derivative of $$\tan{x}$$ is $$\sec^{2}x$$.$7(\tan{x}+x\sec^{2}x)$Done7*(tan(x)+x*sec(x)^2)