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+z3\ln{z}+{z}^{3}?

Here are the steps:



ddzln⁡z+z3\frac{d}{dz} \ln{z}+{z}^{3}

1
Use Sum Rule: ddxf(x)+g(x)=(ddxf(x))+(ddxg(x))\frac{d}{dx} f(x)+g(x)=(\frac{d}{dx} f(x))+(\frac{d}{dx} g(x)).
(ddzln⁡z)+(ddzz3)(\frac{d}{dz} \ln{z})+(\frac{d}{dz} {z}^{3})

2
The derivative of ln⁡x\ln{x} is 1x\frac{1}{x}.
1z+(ddzz3)\frac{1}{z}+(\frac{d}{dz} {z}^{3})

3
Use Power Rule: ddxxn=nxn−1\frac{d}{dx} {x}^{n}=n{x}^{n-1}.
1z+3z2\frac{1}{z}+3{z}^{2}

Done
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