Problem of the Week

Updated at Aug 30, 2021 3:31 PM

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

How would you differentiate \(\cos{z}+\csc{z}\)?

Here are the steps:



\[\frac{d}{dz} \cos{z}+\csc{z}\]

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

2
Use Trigonometric Differentiation: the derivative of \(\cos{x}\) is \(-\sin{x}\).
\[-\sin{z}+(\frac{d}{dz} \csc{z})\]

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

Done
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