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\cos{z}+\csc{z}?

Here are the steps:



ddzcos⁡z+csc⁡z\frac{d}{dz} \cos{z}+\csc{z}

1
Use Sum Rule: ddxf(x)+g(x)=(ddxf(x))+(ddxg(x))\frac{d}{dx} f(x)+g(x)=(\frac{d}{dx} f(x))+(\frac{d}{dx} g(x)).
(ddzcos⁡z)+(ddzcsc⁡z)(\frac{d}{dz} \cos{z})+(\frac{d}{dz} \csc{z})

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

3
Use Trigonometric Differentiation: the derivative of csc⁡x\csc{x} is −csc⁡xcot⁡x-\csc{x}\cot{x}.
−sin⁡z−csc⁡zcot⁡z-\sin{z}-\csc{z}\cot{z}

Done
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