Problem of the Week

Updated at Feb 25, 2019 4:12 PM

How can we find the derivative of \({e}^{x}+{x}^{4}\)?

Below is the solution.



\[\frac{d}{dx} {e}^{x}+{x}^{4}\]

1
Use Sum Rule: \(\frac{d}{dx} f(x)+g(x)=(\frac{d}{dx} f(x))+(\frac{d}{dx} g(x))\).
\[(\frac{d}{dx} {e}^{x})+(\frac{d}{dx} {x}^{4})\]

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

3
Use Power Rule: \(\frac{d}{dx} {x}^{n}=n{x}^{n-1}\).
\[{e}^{x}+4{x}^{3}\]

Done
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