implicit diff.: find dy/dx at (23,6) for 4y^2 - xy - 6 = 0

[Denomination]

If y=y(x) is defined implicitly by 4y^2-xy-6=0 find the value of dy/dx at (23,6).

I got as far as 8y(dy/dx)-x(dy/dx)=0.

I just don't know my next step because I'm not sure if I can move the 8y and -x over because of the fact that it would be dividing zero.

 

[skeeter]

you forgot the product rule for the xy term ...

d/dx[4y² - xy - 6 = 0]

8y(dy/dx) - x(dy/dx) - y = 0

8y(dy/dx) - x(dy/dx) = y

factor out (dy/dx) from both terms ...

(dy/dx)(8y - x) = y

dy/dx = y/(8y - x)

 

[Denomination]

Thanks!

Thanks alot, I can't believe I overlooked that.