Question

How do you implicitly differentiate `x^2+2xy-y^2+x=3`?

Answer 1

`dy/dx = -( (1 + 2x + 2y ))/(2(x - y ))`

Explanation:

Differentiating with respect to x : using the 'product rule' for term 2xy .

2x + `2x d/dx (y ) + y d/dx (2x ) - 2ydy/dx + 1 = 0`

`rArr 2x + 2x dy/dx + 2y - 2y dy/dx + 1 = 0`

`rArr dy/dx ( 2x - 2y ) = - 1 - 2x - 2y`

`rArr dy/dx = - ( 1 + 2x + 2y )/(2 ( x - y ))`