# Problem of the Week

## Updated at Aug 22, 2016 2:02 PM

How can we solve for the derivative of $${x}^{8}{e}^{x}$$?

Below is the solution.

$\frac{d}{dx} {x}^{8}{e}^{x}$

 1 Use Product Rule to find the derivative of $${x}^{8}{e}^{x}$$. The product rule states that $$(fg)'=f'g+fg'$$.$(\frac{d}{dx} {x}^{8}){e}^{x}+{x}^{8}(\frac{d}{dx} {e}^{x})$2 Use Power Rule: $$\frac{d}{dx} {x}^{n}=n{x}^{n-1}$$.$8{x}^{7}{e}^{x}+{x}^{8}(\frac{d}{dx} {e}^{x})$3 The derivative of $${e}^{x}$$ is $${e}^{x}$$.$8{x}^{7}{e}^{x}+{x}^{8}{e}^{x}$Done8*x^7*e^x+x^8*e^x