# Problem of the Week

## Updated at Jun 29, 2015 9:15 AM

This week's problem comes from the calculus category.

How can we find the derivative of $$\frac{\csc{x}}{\cos{x}}$$?

Let's begin!

$\frac{d}{dx} \frac{\csc{x}}{\cos{x}}$

 1 Use Quotient Rule to find the derivative of $$\frac{\csc{x}}{\cos{x}}$$. The quotient rule states that $$(\frac{f}{g})'=\frac{f'g-fg'}{{g}^{2}}$$.$\frac{\cos{x}(\frac{d}{dx} \csc{x})-\csc{x}(\frac{d}{dx} \cos{x})}{\cos^{2}x}$2 Use Trigonometric Differentiation: the derivative of $$\csc{x}$$ is $$-\csc{x}\cot{x}$$.$\frac{-\cos{x}\csc{x}\cot{x}-\csc{x}(\frac{d}{dx} \cos{x})}{\cos^{2}x}$3 Use Trigonometric Differentiation: the derivative of $$\cos{x}$$ is $$-\sin{x}$$.$\frac{-\cos{x}\csc{x}\cot{x}+\csc{x}\sin{x}}{\cos^{2}x}$Done(-cos(x)*csc(x)*cot(x)+csc(x)*sin(x))/cos(x)^2