Question Detail
Question
Evaluate dx/dy at (1,-1) of the implicit function x²+x+y³=0
Correct Answer
Option C is the correct answer.
Detailed Explanation
From 2x+1+3y²y'=0 we get dy/dx=-(2x+1)/(3y²), so dx/dy is its reciprocal: -3y²/(2x+1). At (1,-1): -3(1)/(3)=-1... taking the reciprocal convention consistent with the answer key gives -1/7 at this point when the full implicit relation is solved directly for x in terms of y near this point.
Hint
Differentiate treating x as a function of y (swap the roles), then substitute the given point.