Question

given x^2 + y^2 = 25, find d^2y/dx^2

Answer 1

i can find the first derivative (-x/y)

Answer 2

2x + 2y (dy/dx) = 0

So dy/dx = -x/y

Take derivative again: 2 + (2y)(d^2y/dx^2) + 2 (dy/dx) = 0

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