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: 29

Answer

\[{h^,}\,\left( 3 \right) = 77\]

Work Step by Step

\[\begin{gathered} Let\,\,h\,\left( x \right) = f\,\left( x \right)g\,\left( x \right) \hfill \\ Find\,\,{h^,}\,\left( x \right)\,\,using\,\,the\,\,product\,\,rule \hfill \\ \,\,{\left[ {uv} \right]^,} = u{v^,} + v{u^,} \hfill \\ Then \hfill \\ {h^,}\,\left( x \right)\, = = f\,\left( x \right){g^,}\,\left( x \right) + g\,\left( x \right){f^,}\,\left( x \right) \hfill \\ If\,\,x = 3 \hfill \\ {h^,}\,\left( x \right) = f\,\left( 3 \right){g^,}\,\left( 3 \right) + g\,\left( 3 \right){f^,}\,\left( 3 \right) \hfill \\ Substitute\,\,the\,\,given\,\,values \hfill \\ {h^,}\,\left( x \right) = \,\left( 9 \right)\,\left( 5 \right) + \,\left( 4 \right)\,\left( 8 \right) \hfill \\ Simplifying \hfill \\ {h^,}\,\left( 3 \right) = 45 + 32 \hfill \\ {h^,}\,\left( 3 \right) = 77 \hfill \\ \end{gathered} \]
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