# Math Help - Quick Question on Implicit Differentiation

1. ## Quick Question on Implicit Differentiation

I have the equation:

(x^2)(y^-3) + 3 = y

How do I go about implicitly differentiating this equation?

EDIT: Solve for dy/dx. Sorry about that.

2. Hi, Jeavus. You can probably achieve what this question wants of you, by differentiating both sides of the equation by $x$, assuming that $y$ is some function of $x$:

$x^2 y^{-3} + 3 = y$

$\Rightarrow \frac{d}{dx}\left[x^2 y^{-3} + 3\right] = \frac{d}{dx}\left[y\right] = \frac{dy}{dx}$

$\Rightarrow \left( 2x y^{-3} - 3 x^2 y^{-4} \frac{dy}{dx} \right) = \frac{dy}{dx}$

To do the last step, I used the "product rule" of differentiation.

If you rearrange this, you should be able to work out $\frac{dy}{dx}$ as a function of $x$ and $y$. Hope that helps!