Question

Differentiate implicit function containing product and quotients. d/dx (3x^2 y^3)

Answer 1

6xy^2 + 9(xy)^2.dy/dx

Explanation:

d/dx(3x^2.y^3)=

3y^2.d/dx(x^2) + 3x^2.d/dx(y^3) [Using uv rule, d/dx(uv)=u.dv/dx +v.du/dx]

= 3y^2.2x + 3x^2.3y^2.dy/dx

= 6xy^2 + 9(xy)^2.dy/dx