Calculus with Applications (10th Edition)

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

Chapter 4 - Calculating the Derivative - 4.4 Derivatives of Exponential Functions - 4.4 Exercises: 28

Answer

\[{y^,} = - 6x\ln 10\,\left( {{{10}^{3{x^2} - 4}}} \right)\]

Work Step by Step

\[\begin{gathered} y = - {10^{3{x^2} - 4}} \hfill \\ Find\,\,the\,\,derivative \hfill \\ {y^,} = \,{\left( { - {{10}^{3{x^2} - 4}}} \right)^,} \hfill \\ Use\,\,the\,\,formula \hfill \\ \frac{d}{{dx}}\,\,\left[ {{a^{g\,\left( x \right)}}} \right] = \,\left( {\ln a} \right){a^{g\,\left( x \right)}}{g^,}\,\left( x \right) \hfill \\ Set\,\,a = 10\,,\,g\,\left( x \right) = 3{x^2} - 4 \hfill \\ Then \hfill \\ {y^,} = \, - \,\left( {\ln 10} \right)\,\left( {{{10}^{3{x^2} - 4}}} \right)\,{\left( {3{x^2} - 4} \right)^,} \hfill \\ {y^,} = - \,\left( {\ln 10} \right)\,\left( {{{10}^{3{x^2} - 4}}} \right)\,\left( {6x} \right) \hfill \\ Multiplying \hfill \\ {y^,} = - 6x\ln 10\,\left( {{{10}^{3{x^2} - 4}}} \right) \hfill \\ \end{gathered} \]
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.