Calculus with Applications (10th Edition)

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

Chapter 4 - Calculating the Derivative - 4.2 Derivatives of Products and Quotients - 4.2 Exercises: 12

Answer

\[{f^,}\,\left( x \right) = \frac{{101}}{{\,{{\left( {7x + 3} \right)}^2}}}\]

Work Step by Step

\[\begin{gathered} f\,\left( x \right) = \frac{{8x - 11}}{{7x + 3}} \hfill \\ Use\,\,the\,\,quotient\,\,rule\,\,to\,\,find\,\,{f^,}\,\left( x \right) \hfill \\ {f^,}\,\left( x \right) = \frac{{\,\left( {7x + 3} \right)\,\,{{\left( {8x - 11} \right)}^,} - \,\left( {8x - 11} \right){{\left( {7x + 3} \right)}^,}}}{{{{\left( {7x + 3} \right)}^2}}} \hfill \\ Then \hfill \\ {f^,}\,\left( x \right) = \frac{{\left( {7x + 3} \right)\,\left( 8 \right) - \,\left( {8x - 11} \right)\,\left( 7 \right)}}{{{{\left( {7x + 3} \right)}^2}}} \hfill \\ Simplify\,\,by\,\,multiplying\,\,and\,\,combining\,\,terms \hfill \\ {f^,}\,\left( x \right) = \frac{{56x + 18 - 56x + 77}}{{\,{{\left( {7x + 3} \right)}^2}}} \hfill \\ {f^,}\,\left( x \right) = \frac{{101}}{{\,{{\left( {7x + 3} \right)}^2}}} \hfill \\ \hfill \\ \end{gathered} \]
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