If dy/dx = x²y², then d²y/dx² = ?

Answer 1

f(x,y) = x^2 y^2
df(x,y)/dx = x^2 (2 y dy/dx) + y^2(2 x dx/dx)
but dy/dx = x^2y^2
so
x^2(2 y x^2y^2) + 2 x y^2

2 x^4 y^3 + 2 x y^2

2 x y^2 (x^2 y + 1)