Calculus with Applications (10th Edition)

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

Chapter 4 - Calculating the Derivative - Chapter Review - Review Exercises: 45

Answer

\[{y^,} = - 6x\ln 10\,\left( {{{10}^{ - {x^2}}}} \right)\]

Work Step by Step

\[\begin{gathered} y = 3 \cdot {10^{ - {x^2}}} \hfill \\ Find\,\,the\,\,derivative\,\,of\,\,the\,\,\,function \hfill \\ {y^,} = \,\,{\left[ {3 \cdot {{10}^{ - {x^2}}}} \right]^,} \hfill \\ {y^,} = \,3\,{\left[ {{{10}^{ - {x^2}}}} \right]^,} \hfill \\ Use\,\,the\,\,formula \hfill \\ \frac{d}{{dx}}\,\,\left[ {{a^{g\,\left( x \right)}}} \right] = \,\left( {\ln a} \right){a^{g\,\left( x \right)}}{g^,}\,\left( x \right) \hfill \\ {y^,} = 3\,\left( {\ln 10} \right)\,\left( {{{10}^{ - {x^2}}}} \right)\,\left( { - 2x} \right) \hfill \\ Then \hfill \\ {y^,} = 3\ln 10\,\left( {{{10}^{ - {x^2}}}} \right)\,\left( { - 2x} \right) \hfill \\ {y^,} = - 6x\ln 10\,\left( {{{10}^{ - {x^2}}}} \right) \hfill \\ \hfill \\ \hfill \\ \end{gathered} \]
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