Problem of the Week

Updated at Sep 29, 2014 8:32 AM

How can we solve for the derivative of x2+ex{x}^{2}+{e}^{x}?

Below is the solution.



ddxx2+ex\frac{d}{dx} {x}^{2}+{e}^{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)).
(ddxx2)+(ddxex)(\frac{d}{dx} {x}^{2})+(\frac{d}{dx} {e}^{x})

2
Use Power Rule: ddxxn=nxn−1\frac{d}{dx} {x}^{n}=n{x}^{n-1}.
2x+(ddxex)2x+(\frac{d}{dx} {e}^{x})

3
The derivative of ex{e}^{x} is ex{e}^{x}.
2x+ex2x+{e}^{x}

Done
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