Calc2.33

From Exampleproblems

Find the derivative of $f(x)\,$ with respect to $x\,$ : $f(x)=\frac{\sin^2x}{x^3}\,$

One trick to doing derivatives of quotients is to change them into a product. Here, $\frac{\sin^2x}{x^3}=x^{-3}\sin^2x\,$ , which is a product rule problem.

$f'(x)=[2\sin (x)\cos (x)]x^{-3}+\sin^2(x)(-3)x^{-4}\,$