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## Homework Statement

what s the wrong with the following arguments

suppose that w=f(x,y)and y=x^2

by the chain rule

(for partial derivative )

Dw/Dx=(Dw/Dx)( Dx/Dx)+(Dw/Dy)(Dy/Dx)=Dw/Dx+2x( Dw/Dy)

hence 2x( Dw/Dy)=0 ,and so Dw/Dy=0

## Homework Equations

## The Attempt at a Solution

i think the argument is not right because we can not write Dx/Dx and w has the relationship with x and y ,so we don't need to use Dy/Dx Dx/Dx to get x ,we can do it directly

is there any counterexample ?

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