Problem of the Week

Updated at Nov 16, 2015 12:31 PM

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

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

Here are the steps:



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

1
Use Quotient Rule to find the derivative of \(\frac{\cos{x}}{x}\). The quotient rule states that \((\frac{f}{g})'=\frac{f'g-fg'}{{g}^{2}}\).
\[\frac{x(\frac{d}{dx} \cos{x})-\cos{x}(\frac{d}{dx} x)}{{x}^{2}}\]

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

3
Use Power Rule: \(\frac{d}{dx} {x}^{n}=n{x}^{n-1}\).
\[\frac{-x\sin{x}-\cos{x}}{{x}^{2}}\]

Done
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