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 ex−x{e}^{x}-\sqrt{x}?

Let's start!



ddxex−x\frac{d}{dx} {e}^{x}-\sqrt{x}

1
Use Sum Rule: ddxf(x)+g(x)=(ddxf(x))+(ddxg(x))\frac{d}{dx} f(x)+g(x)=(\frac{d}{dx} f(x))+(\frac{d}{dx} g(x)).
(ddxex)+(ddx−x)(\frac{d}{dx} {e}^{x})+(\frac{d}{dx} -\sqrt{x})

2
The derivative of ex{e}^{x} is ex{e}^{x}.
ex+(ddx−x){e}^{x}+(\frac{d}{dx} -\sqrt{x})

3
Since x=x12\sqrt{x}={x}^{\frac{1}{2}}, using the Power Rule, ddxx12=12x−12\frac{d}{dx} {x}^{\frac{1}{2}}=\frac{1}{2}{x}^{-\frac{1}{2}}
ex−12x{e}^{x}-\frac{1}{2\sqrt{x}}

Done
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