# Problem of the Week

## Updated at Dec 28, 2015 3:43 PM

This week we have another calculus problem:

How would you differentiate $$\frac{5x}{{e}^{x}}$$?

Let's start!

$\frac{d}{dx} \frac{5x}{{e}^{x}}$

 1 Use Constant Factor Rule: $$\frac{d}{dx} cf(x)=c(\frac{d}{dx} f(x))$$.$5(\frac{d}{dx} \frac{x}{{e}^{x}})$2 Use Quotient Rule to find the derivative of $$\frac{x}{{e}^{x}}$$. The quotient rule states that $$(\frac{f}{g})'=\frac{f'g-fg'}{{g}^{2}}$$.$5\times \frac{{e}^{x}(\frac{d}{dx} x)-x(\frac{d}{dx} {e}^{x})}{{e}^{2x}}$3 Use Power Rule: $$\frac{d}{dx} {x}^{n}=n{x}^{n-1}$$.$5\times \frac{{e}^{x}-x(\frac{d}{dx} {e}^{x})}{{e}^{2x}}$4 The derivative of $${e}^{x}$$ is $${e}^{x}$$.$\frac{5({e}^{x}-x{e}^{x})}{{e}^{2x}}$Done(5*(e^x-x*e^x))/e^(2*x)