Problem of the Week

Updated at Mar 27, 2017 3:37 PM

How would you differentiate \(\cos{x}-\cot{x}\)?

Below is the solution.



\[\frac{d}{dx} \cos{x}-\cot{x}\]

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

2
Use Trigonometric Differentiation: the derivative of \(\cos{x}\) is \(-\sin{x}\).
\[-\sin{x}-(\frac{d}{dx} \cot{x})\]

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

Done
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