Differentiate implicitly to find dy/dx, then find the slope at (2,5)
x^2*y-4x^2-4=0

Question

Differentiate implicitly to find dy/dx, then find the slope at (2,5)
x^2*y-4x^2-4=0

lukecrayonz · Answer

@Luigi0210 I got (-2y/x)+(8/x) but what do I do for the slope?:(

loser66 · Answer

i am sorry, that's not right. redo, please

loser66 · Answer

$$(x^2y - 4x^2-4)'\neq -\frac{2y}{x}+\frac{8}{x}$$

anonymous · Answer

Multiply the equation by x^(-2) which is same as dividing by x^2
Then isolate y
Later differentiate the given equation
you will get dy/dx in terms of x...then from given information substitute x=2
You will get the value of dy/dx at (2,5) which is same as the required slope.

loser66 · Answer

try to help, but where is the Asker?

lukecrayonz · Answer

How is it not -2y/x+8/x?
I mean simplified down it's (8-2y)/x

loser66 · Answer

oh yes, you are right, I am so sorry, my bad.
so, you have y ' = 8/x - 2y/x
 just replace(x, y) = ( 2,5) you get y ' = -1
and that is the slope

loser66 · Answer

@Lukecrayonz  I am sorry for my wrongness.

lukecrayonz · Answer

It's okay! Haha

loser66 · Answer

I shouldn't help others right now. I am too busy with my stuff, hihihi... I thought I can relax a little bit by solving the easy stuff but I was wroooooong. XD