# Problem of the Week

## Updated at Feb 1, 2016 1:50 PM

This week's problem comes from the calculus category.

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

Let's begin!

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

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