Implicit differentiation of x²(x-y)²=x²-y²

[Mathos]

Homework Statement

x$$^{}2$$(x-y)$$^{}2$$=x$$^{}2$$-y$$^{}2$$

Homework Equations

The Attempt at a Solution

I can get this far: x[2(x-y)(1-dy/dx)]+2x(x-y)=2x-2ydy/dx

Any small hint as to where to go from here would be much appreciated.

 

[CompuChip]

What is the question?
You posted an equation,
$$x^2(x - y)^2 = x^2 - y^2$$
(and the way you posted it makes me wonder why you did just the superscript in LaTeX which didn't really make it a superscript anymore ) and then went on to write a differential equation.

 

[HallsofIvy]

I assume, CompuChip, that the actual problem was in the title: "implicit differentiation problem". That is, to use implicit differentiation to find dy/dx when $x^2(x-y)^2= x^2- y^2$.

Mathos, it's a real good idea to actually state the problem in the post!

You say you have differentiated to get x[2(x-y)(1-dy/dx)]+2x(x-y)=2x-2ydy/dx (warning: I did not check that!) Now you want to solve that equation for dy/dx. Since differentiation is "linear", that is always a simple linear equation in dy/dx. Go ahead and multiply the left side to get -2x(x-y)dy/dx and add 2y dy/dx to both sides to isolate dy/dx. The divide by its coefficient.

 

[ace123]

Your not supposed to give the answer right away. Your supposed to give clues to how to do it. Ever hear the phrase Give a man a fish; you feed him for a day. Teach a man to fish; you feed him for life.