Implicit Differentiation $x^2 y^3 = 3$ So I've been trying to implicitly differentiate $x^2 y^3 = 3$
which if I use product rule I get
$$
-\frac{2y}{3x}
$$
but when I move $x^2$ to the right hand side and differentiate
I get
$$
-\frac{2}{x^3 y^2} 
$$
which is completely different answer and I do not get what I did wrong.
Help Please.

Beginning with the given equation
$$
x^2 y^3 = 3, 
$$
we can modify the implicit derivative expression to look like the other:
$$
-\frac{2y}{3x} 
= -\frac{2y}{3x} \color{blue}{{}\cdot \frac{x^2 y^2}{x^2 y^2}} 
= -\frac{2x^2 y^3}{3x^3 y^2}
= -\frac{2 \cdot3}{3x^3 y^2}
= -\frac{2}{x^3 y^2}. 
$$
