Calculus with Applications (10th Edition)

Published by Pearson
ISBN 10: 0321749006
ISBN 13: 978-0-32174-900-0

Chapter 6 - Applications of the Derivative - 6.4 Implicit Differentiation - 6.4 Exercises: 2

Answer

\[\frac{{dy}}{{dx}} = \frac{{7x}}{{4y}}\]

Work Step by Step

\[\begin{gathered} 7{x^2} - 4{y^2} = 24 \hfill \\ \,Find\,\,dy/dx\,\,\,by\,\,implicit\,\,differentiation \hfill \\ \frac{{dx}}{{dy}}\,\left( {7{x^2} - 4{y^2}} \right) = \frac{d}{{dx}}\,\left( {24} \right) \hfill \\ 7\,\left( 2 \right){x^{2 - 1}} - 4\,\left( 2 \right){y^{2 - 1}}{y^,} = 0 \hfill \\ 14x - 8y{y^,} = 0 \hfill \\ - 8y{y^,} = - 14x \hfill \\ Divide\,\,by\,\, - 8y \hfill \\ {y^,} = \frac{{ - 14x}}{{ - 8y}} = \frac{{7x}}{{4y}} \hfill \\ Then \hfill \\ \frac{{dy}}{{dx}} = \frac{{7x}}{{4y}} \hfill \\ \end{gathered} \]
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