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: 33

Answer

$\dfrac{d\omega}{d\lambda}=-\dfrac{b^2\lambda}{a^2\omega}$

Work Step by Step

In order to derivate this function you have to apply implicit differentation method. First, take the function to it's $f(\lambda)=0$ form $ a^2\omega^2+b^2\lambda^2-1=0$ Then derivate the whole equation. Rember the put $\omega'$ every time you derivate $\omega$ $2a^2\omega \omega^2 + 2b^2\lambda=0$ Solve for a' and you have the answer $\omega' (2a^2\omega)=-2b^2\lambda$ $\omega '=-\dfrac{b^2\lambda}{a^2\omega}$
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