How do you find (d^2y)/(dx^2) for -4y^2+4=4x^2?

1 Answer
Oct 16, 2016

(d^2y)/dx^2= -1/y^3

Explanation:

Use Implicit Differentiation:

-8y(dy/dx) = 8x

dy/dx = (-x)/y

(d^2y)/dx^2 = d/dx(dy/dx)

(d^2y)/dx^2= (d((-x)/y))/dx

(d^2y)/dx^2= {-y - -x(dy/dx)}/y^2

(d^2y)/dx^2= {(-y^2)/y - -x((-x)/y)}/y^2

(d^2y)/dx^2= -{y^2/y + -x((-x)/y)}/y^2

(d^2y)/dx^2= -{y^2/y + x^2/y}/y^2

(d^2y)/dx^2= -{y^2 + x^2}/y^3

From the original equation, y^2 + x^2 = 1 :

(d^2y)/dx^2= -1/y^3