Problem

(a) Find $ y' $ by implicit differentiation. (b)…

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Problem 1 Easy 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).

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

Answer

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

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Video Transcript

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Related Courses

Calculus 1 / AB

Calculus: Early Transcendentals

Chapter 3

Differentiation Rules

Section 5

Implicit Differentiation

Problem