# Problem of the Week

## Updated at Jan 26, 2015 11:53 AM

This week we have another calculus problem:

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

Let's start!

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

 1 Use Sum Rule: $$\frac{d}{dx} f(x)+g(x)=(\frac{d}{dx} f(x))+(\frac{d}{dx} g(x))$$.$(\frac{d}{dx} {e}^{x})+(\frac{d}{dx} -\sqrt{x})$2 The derivative of $${e}^{x}$$ is $${e}^{x}$$.${e}^{x}+(\frac{d}{dx} -\sqrt{x})$3 Since $$\sqrt{x}={x}^{\frac{1}{2}}$$, using the Power Rule, $$\frac{d}{dx} {x}^{\frac{1}{2}}=\frac{1}{2}{x}^{-\frac{1}{2}}$$${e}^{x}-\frac{1}{2\sqrt{x}}$Donee^x-1/(2*sqrt(x))