Problem of the Week

Updated at Feb 25, 2019 4:12 PM

How can we find the derivative of ex+x4{e}^{x}+{x}^{4}?

Below is the solution.



ddxex+x4\frac{d}{dx} {e}^{x}+{x}^{4}

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)+(ddxx4)(\frac{d}{dx} {e}^{x})+(\frac{d}{dx} {x}^{4})

2
The derivative of ex{e}^{x} is ex{e}^{x}.
ex+(ddxx4){e}^{x}+(\frac{d}{dx} {x}^{4})

3
Use Power Rule: ddxxn=nxn−1\frac{d}{dx} {x}^{n}=n{x}^{n-1}.
ex+4x3{e}^{x}+4{x}^{3}

Done
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