Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 2 - Differentiation - 2.5 Exercises: 23



Work Step by Step

$y^2=\frac{x^2-49}{x^2+49}$ $y^2(x^2+49)=x^2-49$ $x^2y^2+49y^2=x^2-49$ $\frac{d}{dx}[x^2y^2+49y^2]=\frac{d}{dx}[x^2-49]$ $2xy^2+2x^2y\frac{dy}{dx}+98y\frac{dy}{dx}=2x$ $2xy^2+(2x^2y+98y)\frac{dy}{dx}=2x$ $(2x^2y+98y)\frac{dy}{dx}=2x-2xy^2$ $\frac{dy}{dx}=\frac{2x-2xy^2}{2x^2y+98y}$ $\frac{dy}{dx}=\frac{x-xy^2}{x^2y+49y}$ $(7,0)$ $\frac{x-xy^2}{x^2y+49y}=\frac{(7)-(7)(0)^2}{(7)^2(0)+49(0)}=\frac{7}{0}$ Undefined.
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