# Problem of the Week

Updated at Feb 18, 2019 4:06 PM

For this week we've brought you this calculus problem.

How can we find the derivative of $$\ln{z}+{z}^{3}$$?

Here are the steps:

$\frac{d}{dz} \ln{z}+{z}^{3}$

 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}^{3})$2 The derivative of $$\ln{x}$$ is $$\frac{1}{x}$$.$\frac{1}{z}+(\frac{d}{dz} {z}^{3})$3 Use Power Rule: $$\frac{d}{dx} {x}^{n}=n{x}^{n-1}$$.$\frac{1}{z}+3{z}^{2}$Done1/z+3*z^2