Problem of the Week

Updated at Jul 27, 2020 1:28 PM

This week we have another calculus problem:

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

Let's start!



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

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

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

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

Done
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