If you could show me the steps as well, that would be great. I'm totally lost:
find dy/dx
a) x^2 y^2 = x^3-5y
b) x^4 + 3 x^2 y^3 - y^2 = 5
c) x^3 - 6y^2 = 10
thanks so much for your help
I'll work out the last one yeah here we go!
$\displaystyle x^3 - 6y^2 = 10
$
The Key point here is that $\displaystyle y=f(x)$ and that we need to use the chain rule for the derivative.
$\displaystyle \frac{d}{dx}x^3 - \frac{d}{dx}6y^2 = \frac{d}{dx}10$
so taking the derivative we get...
$\displaystyle 3x^2-12y \cdot \frac{dy}{dx}=0$ using the chain rule becuase y is a functin of x.
now we solve for the derivative
$\displaystyle 12y \cdot\frac{dy}{dx}=3x^2 \iff \frac{dy}{dx}=\frac{3x^2}{12}y=\frac{x^2}{4y}$