Question

3. If dy = x^2y^2 , then what is d2y/dx2

Answer 1

`\text{Given that,}\\\\(dy)/(dx) = x^2 y^2\\\\ \implies (d^2 y)/(dx^2) = x^2\cdot 2y (dy)/(dx)+ y^2 \cdot 2x\\\\\implies (d^2 y)/(dx^2) = x^2 \cdot 2y \cdot x^2 y^2 +2xy^2\\\\\implies (d^2 y)/(dx^2) =2x^4y^3 + 2xy^2 = 2xy^2(x^3y+1)`