If dy/dx = x^2y^2, then d^2y/dx^2 =

Dy/dx = x²y²

d²y/dx² = is taking the derivative of the dy/dx

Note that if y = xⁿ,  dy/dx = nxⁿ ⁻ ¹.

For x²y² we will apply product rule of differentiation and implicit differentiation.

Product rule for y = uv

dy/dx = v(du/dx) + u(dv/dx)

dy/dx = x²y²

d²y/dx² = 2xy² + x²*2y*(dy/dx)

d²y/dx² = 2xy² + 2x²y*(dy/dx)

But recall dy/dx = x²y² 

d²y/dx² = 2xy² + 2x²y*(dy/dx)

d²y/dx² = 2xy² + 2x²y*( x²y²)

d²y/dx² = 2xy² + 2x⁴y³ = 2xy²(1 + x³y)

I hope this helps.

The answer would be: b