How do you implicitly differentiate x^2+2xy-y^2+x=3 x2+2xy−y2+x=3?
1 Answer
Jan 18, 2016
dy/dx = -( (1 + 2x + 2y ))/(2(x - y )) dydx=−(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 2xddx(y)+yddx(2x)−2ydydx+1=0
rArr 2x + 2x dy/dx + 2y - 2y dy/dx + 1 = 0 ⇒2x+2xdydx+2y−2ydydx+1=0
rArr dy/dx ( 2x - 2y ) = - 1 - 2x - 2y ⇒dydx(2x−2y)=−1−2x−2y
rArr dy/dx = - ( 1 + 2x + 2y )/(2 ( x - y )) ⇒dydx=−1+2x+2y2(x−y)