The differentiation of $\frac{x^3}{1-x^3}$ w.r.t. $x^3$ is :
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → $\frac{1}{(1-x^3)^2}$
$y=\frac{x^3}{1-x^3}$ $z=x^3$
$\frac{dy}{dx}=\frac{3x^2(1-x^3)}{(1-x^3)^2}+3x^2(x^3)$
$=\frac{3x^2}{(1-x^3)^2}$ $\frac{dz}{dx}=3x^2$
so $\frac{dy}{dz}=\frac{1}{(1-x^3)^2}$