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: 7

Answer

$y' = -\dfrac{y^{3/2}}{x^{3/2}}$

Work Step by Step

In order to derivate this function you have to apply implicit differentation method. First, take the function to it's f(x)=0 form $x^{-1/2}+y^{-1/2}-1=0$ Then derivate the whole equation. Rember the put y' every time you derivate y $-\dfrac{1}{2}x^{-3/2}-\dfrac{1}{2}y^{-3/2}y'=0$ *Note: Here you have to apply the product rule twice Solve for y' and you have the answer $\dfrac{y'}{-2y^{3/2}} =\dfrac{1}{2x^{3/2}}$ $y' = -\dfrac{y^{3/2}}{x^{3/2}}$
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