Problem of the Week

Updated at Mar 28, 2016 3:14 PM

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

How can we solve for the derivative of $${x}^{3}\tan{x}$$?

Check out the solution below!

$\frac{d}{dx} {x}^{3}\tan{x}$

 1 Use Product Rule to find the derivative of $${x}^{3}\tan{x}$$. The product rule states that $$(fg)'=f'g+fg'$$.$(\frac{d}{dx} {x}^{3})\tan{x}+{x}^{3}(\frac{d}{dx} \tan{x})$2 Use Power Rule: $$\frac{d}{dx} {x}^{n}=n{x}^{n-1}$$.$3{x}^{2}\tan{x}+{x}^{3}(\frac{d}{dx} \tan{x})$3 Use Trigonometric Differentiation: the derivative of $$\tan{x}$$ is $$\sec^{2}x$$.$3{x}^{2}\tan{x}+{x}^{3}\sec^{2}x$Done3*x^2*tan(x)+x^3*sec(x)^2