# 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: $$\frac{d}{dx} {x}^{n}=n{x}^{n-1}$$.$\frac{1}{z}+7{z}^{6}$Done1/z+7*z^6