Question

x^3+y^3=3abxy find d^2y/dx^2

Answer 1

y^3=x^4
d/dx[y^3]=d/dx[x^4]
(3y^2)(dy/dx)=4x^3
dy/dx=(4x^3/3y^2)(xy/xy)
dy/dx=(4y/3x)(x^4/y^3)
dy/dx=4y/3x
d^2y/dx^2=(d/dx)(4y/3x)
d^2y/dx^2=[(4)(dy/dx)(3x)-(4y)(3)]/9x^2
And by substituting 4y/3x for dy/dx:
d^2y/dx^2=(4y/9x^2)(xy/xy)
d^2y/dx^2=(4x/9y)(y^2/x^3)
d^2y/dx^2=4x/9y