# 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(-x*sin(x)-cos(x))/(2*x^2)