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 cos⁡x2x\frac{\cos{x}}{2x}?

Check out the solution below!



ddxcos⁡x2x\frac{d}{dx} \frac{\cos{x}}{2x}

1
Use Constant Factor Rule: ddxcf(x)=c(ddxf(x))\frac{d}{dx} cf(x)=c(\frac{d}{dx} f(x)).
12(ddxcos⁡xx)\frac{1}{2}(\frac{d}{dx} \frac{\cos{x}}{x})

2
Use Quotient Rule to find the derivative of cos⁡xx\frac{\cos{x}}{x}. The quotient rule states that (fg)′=f′g−fg′g2(\frac{f}{g})'=\frac{f'g-fg'}{{g}^{2}}.
12×x(ddxcos⁡x)−cos⁡x(ddxx)x2\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\cos{x} is −sin⁡x-\sin{x}.
12×−xsin⁡x−cos⁡x(ddxx)x2\frac{1}{2}\times \frac{-x\sin{x}-\cos{x}(\frac{d}{dx} x)}{{x}^{2}}

4
Use Power Rule: ddxxn=nxn−1\frac{d}{dx} {x}^{n}=n{x}^{n-1}.
−xsin⁡x−cos⁡x2x2\frac{-x\sin{x}-\cos{x}}{2{x}^{2}}

Done
Cymath foriOSAndroid