# Math Help - Implict functions

1. ## Implict functions

When doing these I am unsure of where to place dy/dx

for example of this problem

$x^2+xy-y^3=xy^2$

2. Originally Posted by sk8erboyla2004
When doing these I am unsure of where to place dy/dx

for example of this problem

$x^2+xy-y^3=xy^2$

If you are using implicit differentiation, take the derivative with respect to x of both sides. When you come across something with a y, use the chain rule.

You should end up with something that has $\frac{dy}{dx}$ in it, and then make $\frac{dy}{dx}$ the subject.

$\frac{d}{dx}(x^2 + xy - y^3) = \frac{d}{dx}(xy^2)$
$\frac{d}{dx}(x^2) + \frac{d}{dx}(xy) - \frac{d}{dx}(y^3) = \frac{d}{dx}(xy^2)$
$2x + x\frac{dy}{dx} + y - 3y^2\frac{dy}{dx} = y^2 + 2xy\frac{dy}{dx}$
Now just make $\frac{dy}{dx}$ the subject.