Problem of the Week

Updated at Nov 3, 2025 4:25 PM

This week's problem comes from the calculus category.

How would you differentiate \(2t+\cot{t}\)?

Let's begin!



\[\frac{d}{dt} 2t+\cot{t}\]

1
Use Sum Rule: \(\frac{d}{dx} f(x)+g(x)=(\frac{d}{dx} f(x))+(\frac{d}{dx} g(x))\).
\[(\frac{d}{dt} 2t)+(\frac{d}{dt} \cot{t})\]

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

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

Done
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