# Thread: Second Derivative using Implicit Differentiation

1. ## Second Derivative using Implicit Differentiation

So we are asked to find the second derivative (implicitly) of : x^2y^2-6x=7
So far I've been able to find the first derivative no problem.
My first derivative is: -(x*y^2 + 3) / y*x^2
I've verified this against two different online implicit differentiation calculators so I know I'm right to this point.
However I need to take the derivative of this first derivative to reach my goal.
I can not figure it out. Below I'll include two answers that have so far been marked wrong by webassign.net
a) -(y^3*x - 6y) / x(-y^2*x + 3)

b) (x*y^2 + 6) / (x^3*y)

2. ## Re: Second Derivative using Implicit Differentiation

actually you have a sign error in the first derivative

to find the 2nd derivative just differentiate your expression for $y'$ again.

You'll need to use the quotient rule.

When you've done all that and simplified it solve for $y''$

I get

$y''(x)= \dfrac{-x^2 y(x)^2 y'(x)-3 x y'(x)+x y(x)^3-6 y(x)}{x^3 y(x)^2}$