Question

how do you find d^2y/dx^2 of x^2+y^2=1

Answer 1

x^2+y^2=1


d/dx(x^2+y^2)=d/dx(1)


2x+2y*y' = 0


2y*y' = -2x


y' = -2x/2y


y' = -x/y


So the first derivative wrt x is y' = -x/y


Now derive both sides again


y' = -x/y


d/dx(y') = d/dx(-x/y)


y'' = d/dx(-xy^(-1))


y'' = -y^(-1) + xy^(-2)*y'


y'' = -y^(-1) + xy^(-2)*(-x/y)


y'' = -1/y - x^2/y^3


y'' = (-y - x^2)/(y^3)


y'' = -(x^2+y)/(y^3)


So the second derivative wrt x is y'' = -(x^2+y)/(y^3)

Answer 2

Thank you!

Answer 3

np