APFIVE Implicit Differentiation Error Analysis
When differentiating the equation $$xy + y^2 = 10$$ with respect to x, a student obtains the incorrect result $$y + y' + 2yy' = 0$$. Which statement best identifies the error in the student’s process?
A
The error is in differentiating y^2 rather than xy.
B
The student omitted the product rule for xy; the correct differentiation is x*(dy/dx) + y + 2y(dy/dx) = 0, so that dy/dx = -y/(x + 2*y).
C
She should have treated xy + y^2 as a constant multiple of y.
D
There is no mistake; her differentiation is correct.
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