Problem of the Week

Updated at Feb 20, 2023 5:57 PM

How can we find the derivative of \(\ln{z}+{z}^{7}\)?

Below is the solution.



\[\frac{d}{dz} \ln{z}+{z}^{7}\]

1
Use Sum Rule: \(\frac{d}{dx} f(x)+g(x)=(\frac{d}{dx} f(x))+(\frac{d}{dx} g(x))\).
\[(\frac{d}{dz} \ln{z})+(\frac{d}{dz} {z}^{7})\]

2
The derivative of \(\ln{x}\) is \(\frac{1}{x}\).
\[\frac{1}{z}+(\frac{d}{dz} {z}^{7})\]

3
Use Power Rule: \(\frac{d}{dx} {x}^{n}=n{x}^{n-1}\).
\[\frac{1}{z}+7{z}^{6}\]

Done
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