Calculus, 10th Edition (Anton)

Published by Wiley
ISBN 10: 0-47064-772-8
ISBN 13: 978-0-47064-772-1

Chapter 2 - The Derivative - 2.7 Implicit Differentiation - Exercises Set 2.7 - Page 167: 49

Answer

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Work Step by Step

With an explicit definition, the function is only written in terms of one variable. For example, $f(x) = x^2$ is only written in terms of $x$. Instead, an implicit definition results in both the input and output variables being present in an equation. For example, $x^2+y^2 = 1$ has both $x$ and $y$ appear in the equation to denote a circle. Both implicit and explicit definitions define functions and can define equal functions; the difference is a matter of notation and what variables are present in the definition of the function.
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