Problem of the Week

Updated at Apr 10, 2017 2:24 PM

To get more practice in calculus, we brought you this problem of the week:

How can we find the derivative of x6+ex{x}^{6}+{e}^{x}?

Check out the solution below!



ddxx6+ex\frac{d}{dx} {x}^{6}+{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)).
(ddxx6)+(ddxex)(\frac{d}{dx} {x}^{6})+(\frac{d}{dx} {e}^{x})

2
Use Power Rule: ddxxn=nxn−1\frac{d}{dx} {x}^{n}=n{x}^{n-1}.
6x5+(ddxex)6{x}^{5}+(\frac{d}{dx} {e}^{x})

3
The derivative of ex{e}^{x} is ex{e}^{x}.
6x5+ex6{x}^{5}+{e}^{x}

Done
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