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Problem 2 Medium Difficulty

(a) Find $ y' $ by implicit differentiation.
(b) Solve the equation explicitly for y and differentiate to get $ y' $ in terms of $ x. $
(c) Check that your solutions to part (a) and (b) are consistent by substituting the expression for $ y $ into your solution for part (a).

$ 2x^2 + x + xy = 1 $

Answer

a. $\frac{-(4 x+1+y)}{x}$
b. $\frac{-2 x^{2}-1}{x^{2}}$
c. See explanation

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Video Transcript

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