Problem of the Week

Updated at Oct 27, 2025 11:01 AM

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

How would you differentiate \(\csc{w}+{w}^{8}\)?

Here are the steps:



\[\frac{d}{dw} \csc{w}+{w}^{8}\]

1
Use Sum Rule: \(\frac{d}{dx} f(x)+g(x)=(\frac{d}{dx} f(x))+(\frac{d}{dx} g(x))\).
\[(\frac{d}{dw} \csc{w})+(\frac{d}{dw} {w}^{8})\]

2
Use Trigonometric Differentiation: the derivative of \(\csc{x}\) is \(-\csc{x}\cot{x}\).
\[-\csc{w}\cot{w}+(\frac{d}{dw} {w}^{8})\]

3
Use Power Rule: \(\frac{d}{dx} {x}^{n}=n{x}^{n-1}\).
\[-\csc{w}\cot{w}+8{w}^{7}\]

Done
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