Problem of the Week

Updated at Feb 2, 2026 2:46 PM

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

How would you differentiate \(8u+\cot{u}\)?

Here are the steps:



\[\frac{d}{du} 8u+\cot{u}\]

1
Use Sum Rule: \(\frac{d}{dx} f(x)+g(x)=(\frac{d}{dx} f(x))+(\frac{d}{dx} g(x))\).
\[(\frac{d}{du} 8u)+(\frac{d}{du} \cot{u})\]

2
Use Power Rule: \(\frac{d}{dx} {x}^{n}=n{x}^{n-1}\).
\[8+(\frac{d}{du} \cot{u})\]

3
Use Trigonometric Differentiation: the derivative of \(\cot{x}\) is \(-\csc^{2}x\).
\[8-\csc^{2}u\]

Done
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