Implicit Differentiation Understanding Question?

Answer 1

Your expressions are incorrect

d(2xy)/dx = 2d(xy)/dx

= 2{ d(x)*y/dx + x*d(y)/dx) ............ product rule

= 2{ 1 * y + x*dy/dx}

= 2y + 2xdy/dx

d(xy)/dx = y dx/dx + xdy/dx ...........product rule

= y*1 + xdy/dx

= y + xdy/dx

Answer 2

It's not. The derivative of xy would be y + xdy/dx. Use the Product Rule and remember that y may be a function of x

Answer 3

dsd un moneto