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(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).

$ 9 x^2 - y^2 = 1 $

a. $\frac{9 x}{y}$b. $\pm \frac{9 x}{\sqrt{9 x^{2}-1}}$c. From part $(a), y^{\prime}=\frac{9 x}{y}=\frac{9 x}{\pm \sqrt{9 x^{2}-1}},$ which agrees with part

00:48

Frank L.

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 5

Implicit Differentiation

Derivatives

Differentiation

Missouri State University

Oregon State University

Harvey Mudd College

Idaho State University

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