Problem of the Week

Updated at Aug 5, 2013 5:46 PM

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

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

Here are the steps:



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

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

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

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

Done
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