Problem of the Week

Updated at Jun 1, 2026 9:36 AM

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

How can we find the derivative of \({z}^{5}+\sin{z}\)?

Here are the steps:



\[\frac{d}{dz} {z}^{5}+\sin{z}\]

1
Use Sum Rule: \(\frac{d}{dx} f(x)+g(x)=(\frac{d}{dx} f(x))+(\frac{d}{dx} g(x))\).
\[(\frac{d}{dz} {z}^{5})+(\frac{d}{dz} \sin{z})\]

2
Use Power Rule: \(\frac{d}{dx} {x}^{n}=n{x}^{n-1}\).
\[5{z}^{4}+(\frac{d}{dz} \sin{z})\]

3
Use Trigonometric Differentiation: the derivative of \(\sin{x}\) is \(\cos{x}\).
\[5{z}^{4}+\cos{z}\]

Done
Cymath foriOSAndroid