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, \(\frac{d}{dx} {x}^{\frac{1}{2}}=\frac{1}{2}{x}^{-\frac{1}{2}}\)
\[{e}^{x}-\frac{1}{2\sqrt{x}}\]

Done
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