Answer
$a.\frac{12x^2+12}{x^3}$ and $d.12x^3+12x^{-3}$ do not equal $\frac{d}{dx}(4x^3-6x^{-2})$
Work Step by Step
$\frac{d}{dx}(4x^3-6x^{-2})=12x^2+12x^{-3}$
a. $\frac{12x^2+12}{x^3}=\frac{12}{x}+\frac{12}{x^3}=12x^{-1}+12x^{-3}$
b. $\frac{12x^5+12}{x^3}=12x^2+\frac{12}{x^3}=12x^2+12x^{-3}$
c. $12x^2+\frac{12}{x^3}=12x^2+12x^{-3}$
d. $12x^3+12x^{-3}$
So the correct answers are $b.\frac{12x^5+12}{x^3}$ and $c. 12x^2+\frac{12}{x^3}=12x^2+12x^{-3}$
