What is 2xy differentiated implicitly?

2 Answers
Sep 2, 2015

#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)#

Jul 20, 2018

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#