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: 32

Answer

$\dfrac{du}{dv}=-\dfrac{\sqrt{u}}{\sqrt{v}}$

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(v)=0 form $ u^{1/2}+v^{1/2}-5=0$ Then derivate the whole equation. Rember the put u' every time you derivate u $\dfrac{1}{2}u^{-1/2}+\dfrac{1}{2}v^{-1/2}=0$ Solve for a' and you have the answer $\dfrac{u'}{2\sqrt{u}} = \dfrac{-1}{2\sqrt{v}}$ $u'=-\dfrac{\sqrt{u}}{\sqrt{v}}$
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