Question

evaluate when x=-2
d/dx[(3x^2-2)^3/(2x+3)^3]
can some one help me with this I am struggling with derivatives

Answer 1

\[\rm \frac{d}{dx}\frac{(3x^2-2)^3}{(2x+3)^3}\quad=\quad \frac{\color{royalblue}{\left[(3x^2-2)^3\right]'}(2x+3)^3-(3x^2-2)^3\color{royalblue}{\left[(2x+3)^3\right]'}}{(2x+3)^3}\]I guess you would want to start by `setting up` your quotient rule, ya?
You can skip the set up step if you're comfortable with doing so.

But early on in your calculus studies, it's a good practice to use.

Answer 2

As I've set up here, the blue parts are the derivatives that we need to take.
Power rule into chain rule.

Answer 3

thats what I got.. is this correct?