How do you implicitly differentiate x^2+2xy-y^2+x=3 x2+2xyy2+x=3?

1 Answer
Jan 18, 2016

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

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 2xddx(y)+yddx(2x)2ydydx+1=0

rArr 2x + 2x dy/dx + 2y - 2y dy/dx + 1 = 0 2x+2xdydx+2y2ydydx+1=0

rArr dy/dx ( 2x - 2y ) = - 1 - 2x - 2y dydx(2x2y)=12x2y

rArr dy/dx = - ( 1 + 2x + 2y )/(2 ( x - y )) dydx=1+2x+2y2(xy)