Question

What is 2xy differentiated implicitly?

Answer 1

`y'=(2y)/(1-2x)`

Explanation:

The question does not specify with respect to what so I'll assume y is a function of x.

Use the product rule:

`y' = d((u.v))/dx=v.du/dx+u.dv/dx`

So:

`y'=2x.y'+y2.dx/dx`

`y'=2x.y'+2y`

`y'=(2y)/(1-2x)`

Answer 2

The answer is `=-y/x`

Explanation:

The function is

`f(x,y)=2xy`

The partial derivatives are

`(delf)/(delx)=2y`

`(delf)/(dely)=2x`

Therefore,

`dy/dx=-((delf)/(delx))/((delf)/(dely))=-(2y)/(2x)=-y/x`