Problem of the Week

Updated at Dec 5, 2016 2:19 PM

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

How would you differentiate \(\frac{\cos{x}}{2x}\)?

Check out the solution below!



\[\frac{d}{dx} \frac{\cos{x}}{2x}\]

1
Use Constant Factor Rule: \(\frac{d}{dx} cf(x)=c(\frac{d}{dx} f(x))\).
\[\frac{1}{2}(\frac{d}{dx} \frac{\cos{x}}{x})\]

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

3
Use Trigonometric Differentiation: the derivative of \(\cos{x}\) is \(-\sin{x}\).
\[\frac{1}{2}\times \frac{-x\sin{x}-\cos{x}(\frac{d}{dx} x)}{{x}^{2}}\]

4
Use Power Rule: \(\frac{d}{dx} {x}^{n}=n{x}^{n-1}\).
\[\frac{-x\sin{x}-\cos{x}}{2{x}^{2}}\]

Done
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