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Problem 4 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).

$ \frac {2}{x} - \frac {1}{y} = 4 $

Answer

a. $\frac{d y}{d x}=\frac{2 \cdot y^{2}}{x^{2}}$
b. $y^{\prime}=\frac{1}{2(1-2 x)^{2}}$
c. click for solution

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Video Transcript

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