# Problem of the Week

## Updated at Dec 21, 2015 9:27 AM

How can we find the derivative of $$\frac{1}{\sin^{2}x}$$?

Below is the solution.

$\frac{d}{dx} \frac{1}{\sin^{2}x}$

 1 Use Chain Rule on $$\frac{d}{dx} \frac{1}{\sin^{2}x}$$. Let $$u=\sin{x}$$. Use Power Rule: $$\frac{d}{du} {u}^{n}=n{u}^{n-1}$$.$-\frac{2}{\sin^{3}x}(\frac{d}{dx} \sin{x})$2 Use Trigonometric Differentiation: the derivative of $$\sin{x}$$ is $$\cos{x}$$.$-\frac{2\cos{x}}{\sin^{3}x}$Done-(2*cos(x))/sin(x)^3