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 :)

Printable View

- Mar 24th 2008, 09:18 AMshepherdm1270Implicit Differentiation
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 :) - Mar 24th 2008, 09:39 AMTheEmptySetpart c
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

$\displaystyle 12y \cdot\frac{dy}{dx}=3x^2 \iff \frac{dy}{dx}=\frac{3x^2}{12}y=\frac{x^2}{4y}$