WAEC Further Mathematics 2023 Objective — Question 31

Question 31 of 40 from the West African Examinations Council (WAEC) Further Mathematics 2023 Objective paper, with the correct answer and a full explanation.

If y^2+2xy-8=0, find dy/dx.

A. dy/dx=(2y+x)/y
B. dy/dx=(2y-x)/-y
C. dy/dx=-y/(y+x)Correct
D. dy/dx=y/(2y-x)

Explanation

Differentiating implicitly (product rule on 2xy): 2y(dy/dx)+2[x(dy/dx)+y]=0 => (2y+2x)(dy/dx)=-2y => dy/dx=-2y/(2(y+x))=-y/(y+x).

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