Question Detail
Question
Find dy/dx of the implicit function x²y + x(y+1)² = 2 at (x,y) = (1,1)
Correct Answer
Option C is the correct answer.
Detailed Explanation
Differentiating implicitly: 2xy + x²y' + (y+1)² + x·2(y+1)y' = 0. At (1,1): 2(1)(1)+1·y'+4+1·2(2)y'=0 → 2+y'+4+4y'=0 → 5y'=-6 → y'=-6/5.
Hint
Differentiate every term with respect to x, remembering the product and chain rules for terms containing y, then substitute x=1, y=1.