# Problem of the Week

## Updated at May 19, 2014 11:07 AM

How would you differentiate $$\frac{5}{8\cos{x}}$$?

Below is the solution.

$\frac{d}{dx} \frac{5}{8\cos{x}}$

 1 Use Constant Factor Rule: $$\frac{d}{dx} cf(x)=c(\frac{d}{dx} f(x))$$.$\frac{5}{8}(\frac{d}{dx} \frac{1}{\cos{x}})$2 Use Chain Rule on $$\frac{d}{dx} \frac{1}{\cos{x}}$$. Let $$u=\cos{x}$$. Use Power Rule: $$\frac{d}{du} {u}^{n}=n{u}^{n-1}$$.$\frac{5}{8}\times \frac{-1}{\cos^{2}x}(\frac{d}{dx} \cos{x})$3 Use Trigonometric Differentiation: the derivative of $$\cos{x}$$ is $$-\sin{x}$$.$\frac{5\sin{x}}{8\cos^{2}x}$Done(5*sin(x))/(8*cos(x)^2)