# `x^2 + xy - y^2 = 4` Find `(dy/dx)` by implicit differentiation.

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### 2 Answers

*Note:- 1) If y = x^n ; then dy/dx = n*x^(n-1) ; where 'n' = real number *

*2) If y = u*v ; where both u & v are functions of 'x' ; then*

*dy/dx = u*(dv/dx) + v*(du/dx)*

*3) If y = k ; where k = constant ; then dy/dx = 0*

Now, the given function is :-

*(x^2) + xy - (y^2) = 4*

*Differentiating both sides w.r.t 'x' we get,*

*2x + x*(dy/dx) + y - 2y*(dy/dx) = 0*

*or, (2x+y) = (2y-x)*(dy/dx)*

*or, dy/dx = (2x+y)/(2y-x)*

`x^2+xy-y^2=4`

Differentiating with respect to x. We get

`2x+(y+x(dy/dx))-2y(dy/dx)=0`

`(2x+y)+(x-2y)(dy/dx)=0`

`dy/dx=(2y-x)/(2x+y)`