# Problem of the Week

## Updated at Feb 15, 2016 1:34 PM

To get more practice in calculus, we brought you this problem of the week:

How would you differentiate $$6x\sec{x}$$?

Check out the solution below!

$\frac{d}{dx} 6x\sec{x}$

 1 Use Constant Factor Rule: $$\frac{d}{dx} cf(x)=c(\frac{d}{dx} f(x))$$.$6(\frac{d}{dx} x\sec{x})$2 Use Product Rule to find the derivative of $$x\sec{x}$$. The product rule states that $$(fg)'=f'g+fg'$$.$6((\frac{d}{dx} x)\sec{x}+x(\frac{d}{dx} \sec{x}))$3 Use Power Rule: $$\frac{d}{dx} {x}^{n}=n{x}^{n-1}$$.$6(\sec{x}+x(\frac{d}{dx} \sec{x}))$4 Use Trigonometric Differentiation: the derivative of $$\sec{x}$$ is $$\sec{x}\tan{x}$$.$6(\sec{x}+x\sec{x}\tan{x})$Done6*(sec(x)+x*sec(x)*tan(x))