# Problem of the Week

## Updated at Jan 16, 2017 1:47 PM

How can we solve for the derivative of $$9x\cos{x}$$?

Below is the solution.

$\frac{d}{dx} 9x\cos{x}$

 1 Use Constant Factor Rule: $$\frac{d}{dx} cf(x)=c(\frac{d}{dx} f(x))$$.$9(\frac{d}{dx} x\cos{x})$2 Use Product Rule to find the derivative of $$x\cos{x}$$. The product rule states that $$(fg)'=f'g+fg'$$.$9((\frac{d}{dx} x)\cos{x}+x(\frac{d}{dx} \cos{x}))$3 Use Power Rule: $$\frac{d}{dx} {x}^{n}=n{x}^{n-1}$$.$9(\cos{x}+x(\frac{d}{dx} \cos{x}))$4 Use Trigonometric Differentiation: the derivative of $$\cos{x}$$ is $$-\sin{x}$$.$9(\cos{x}-x\sin{x})$Done9*(cos(x)-x*sin(x))