Problem of the Week

Updated at Nov 22, 2021 3:12 PM

How can we find the derivative of \({e}^{y}+{y}^{6}\)?

Below is the solution.



\[\frac{d}{dy} {e}^{y}+{y}^{6}\]

1
Use Sum Rule: \(\frac{d}{dx} f(x)+g(x)=(\frac{d}{dx} f(x))+(\frac{d}{dx} g(x))\).
\[(\frac{d}{dy} {e}^{y})+(\frac{d}{dy} {y}^{6})\]

2
The derivative of \({e}^{x}\) is \({e}^{x}\).
\[{e}^{y}+(\frac{d}{dy} {y}^{6})\]

3
Use Power Rule: \(\frac{d}{dx} {x}^{n}=n{x}^{n-1}\).
\[{e}^{y}+6{y}^{5}\]

Done
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