# Problem of the Week

## Updated at Sep 1, 2014 8:36 AM

For this week we've brought you this calculus problem.

How can we find the derivative of $${x}^{6}+\cos{x}$$?

Here are the steps:

$\frac{d}{dx} {x}^{6}+\cos{x}$

 1 Use Sum Rule: $$\frac{d}{dx} f(x)+g(x)=(\frac{d}{dx} f(x))+(\frac{d}{dx} g(x))$$.$(\frac{d}{dx} {x}^{6})+(\frac{d}{dx} \cos{x})$2 Use Power Rule: $$\frac{d}{dx} {x}^{n}=n{x}^{n-1}$$.$6{x}^{5}+(\frac{d}{dx} \cos{x})$3 Use Trigonometric Differentiation: the derivative of $$\cos{x}$$ is $$-\sin{x}$$.$6{x}^{5}-\sin{x}$Done6*x^5-sin(x)