Question

if y^2=(x-a)(x-b) show that d^3/dx^3[(d^2y/dx^2)^-2/3=0​

Answer 1

Step-by-step explanation:

dy/dx = 1/(dx/dy)

(d^2 y)/dx^2 = d/dx (1/(dx/dy))dy/dx

= d/dy(1/(dx/dy))dy/dx

(d^2y)/(dx^2)= -1/(dx/dy)^2 (d^2x)/dy^2dy/dx

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

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