Problem of the Week

Updated at Oct 27, 2014 9:11 AM

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

How can we solve for the derivative of \(\cot{x}\cos{x}\)?

Here are the steps:



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

1
Use Product Rule to find the derivative of \(\cot{x}\cos{x}\). The product rule states that \((fg)'=f'g+fg'\).
\[(\frac{d}{dx} \cot{x})\cos{x}+\cot{x}(\frac{d}{dx} \cos{x})\]

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

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

Done
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