# Problem of the Week

## Updated at Dec 1, 2014 5:25 PM

This week's problem comes from the calculus category.

How would you differentiate $$\cos{x}-\sin{x}$$?

Let's begin!

$\frac{d}{dx} \cos{x}-\sin{x}$

 1 Use Sum Rule: $$\frac{d}{dx} f(x)+g(x)=(\frac{d}{dx} f(x))+(\frac{d}{dx} g(x))$$.$(\frac{d}{dx} \cos{x})-(\frac{d}{dx} \sin{x})$2 Use Trigonometric Differentiation: the derivative of $$\cos{x}$$ is $$-\sin{x}$$.$-\sin{x}-(\frac{d}{dx} \sin{x})$3 Use Trigonometric Differentiation: the derivative of $$\sin{x}$$ is $$\cos{x}$$.$-\sin{x}-\cos{x}$Done-sin(x)-cos(x)