Problem of the Week

Updated at Feb 10, 2025 12:04 PM

To get more practice in calculus, we brought you this problem of the week:

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

Check out the solution below!



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

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

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

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

Done
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