# Problem of the Week

## Updated at Feb 23, 2015 1:13 PM

This week we have another calculus problem:

How would you differentiate $${x}^{7}-{e}^{x}$$?

Let's start!

$\frac{d}{dx} {x}^{7}-{e}^{x}$

 1 Use Sum Rule: $$\frac{d}{dx} f(x)+g(x)=(\frac{d}{dx} f(x))+(\frac{d}{dx} g(x))$$.$(\frac{d}{dx} {x}^{7})-(\frac{d}{dx} {e}^{x})$2 Use Power Rule: $$\frac{d}{dx} {x}^{n}=n{x}^{n-1}$$.$7{x}^{6}-(\frac{d}{dx} {e}^{x})$3 The derivative of $${e}^{x}$$ is $${e}^{x}$$.$7{x}^{6}-{e}^{x}$Done7*x^6-e^x