Question

x^2 + y^2 = 4, find d^2y/dx^2

Answer 1

i can find the first derivative, -x/y
and i know the answer should be 4/y^3

Answer 2

are you using implicit differentiation yet?

Answer 3

yeah thats exactly it, sorry i can find differnetiations and i know i'm supposed to differntiate my differentiation but it won't come out properly

Answer 4

dy/dx -> 2x + 2y * (dy/dx) = 0
dy /dx = -x/y
d^2y / dx^2 -> 2 + 2 * (dy/dx * dy/dx + y * (d^2y/ dx^2)) =0
2 + 2 * ((dy/dx)^2 + y * (d^2y/dx^2)) = 0
2 + 2 * (x^2/y^2 + y * d^2y/dx^2) =0
-(1 + x^2/y^2) / y = d^2y/dx^2
-(y^2 + x^2) / y^3
y^2 = 4-x^2 so :
-(4-x^2 + x^2) / y^3 = -4/y^3