Problem of the Week

Updated at Nov 14, 2016 2:59 PM

To get more practice in calculus, we brought you this problem of the week:

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

Check out the solution below!



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

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

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

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

Done
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