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