The correct option is D −82227
Differentiating the given expression, we get
3x2−4xy2−4x2yy′+5+y′=0
Putting x = 1, we have
3.1−4.1.1−4.1.1y′(1)+5+y′(1)=0
⇒4−3y′(1)=0⇒y′(1)=43
Differentiating again, we have
6x−4y2−8xyy′−8xyy′−4x2(y′)2−4x2yy′′+y′′=0
Putting x = 1, y = 1 and y′(1)=43, we get
6−4−8(43)−8(43)−4(169)−3y′′(1)=0
⇒y′′(1)=−82227