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

for example of this problem

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

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- Mar 21st 2009, 07:36 PMsk8erboyla2004Implict functions
When doing these I am unsure of where to place dy/dx

for example of this problem

$\displaystyle x^2+xy-y^3=xy^2$ - Mar 21st 2009, 07:55 PMProve It

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 $\displaystyle \frac{dy}{dx}$ in it, and then make $\displaystyle \frac{dy}{dx}$ the subject.

Using your example...

$\displaystyle \frac{d}{dx}(x^2 + xy - y^3) = \frac{d}{dx}(xy^2)$

$\displaystyle \frac{d}{dx}(x^2) + \frac{d}{dx}(xy) - \frac{d}{dx}(y^3) = \frac{d}{dx}(xy^2)$

$\displaystyle 2x + x\frac{dy}{dx} + y - 3y^2\frac{dy}{dx} = y^2 + 2xy\frac{dy}{dx}$

Now just make $\displaystyle \frac{dy}{dx}$ the subject.