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MATH 2163 Lecture 13: Product and chain rule

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Calculus III

Mathematics

Mandlik

Oklahoma State University

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Survey of American History

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<div style="font-family:'Helvetica Neue', Helvetica, Arial;color:#333333;"> Differential Equations and Complex Analysis <div> <br> <picture><source srcset="https://prealliance-textbook-qa.oneclass.com/qa_images/homework_help/question/qa_images/72/7293465.jpeg" type="image/webp"></source><img src="https://prealliance-textbook-qa.oneclass.com/qa_images/homework_help/question/qa_images/72/7293465.jpeg" alt=""></picture> </div> </div> <div id="esf" class="hidden">2, Let f = u+iv be an analytic function with real part u(x, y) 3 exp x cos y +4x Compute v(x, y), f(z), and f(z). Last modified: Wednesday, 22 November 2017, 5:29 PM </div>

<p></p><p>Use the Chain Rule and the Product Rule to give an alternate proof of the Quotient Rule.</p><p>[Hint: Write<img src="data:image/png;base64,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" class="fm-editor-equation" data-mlang="latex" data-equation="%5Cfrac%7Bf%28x%29%7D%7Bg%28x%29%7D%3Df%28x%29lbrackg%28x%29rbrack%5E%7B-1%7D">.]</p>

<p>Use the Chain Rule and the Product Rule to give an alternative proof of the Quotient Rule. </p>
<p>Hint: Write <picture><source srcset="https://s3.amazonaws.com/prealliance-textbook-qa.oneclass.com/qa_images/homework_help/question/qa_images/225862302273245/question/0.webp?img=a38f48d06b7d45cc2acf78214370ce03" type="image/webp"><img src="https://s3.amazonaws.com/prealliance-textbook-qa.oneclass.com/qa_images/homework_help/question/qa_images/225862302273245/question/0.png?img=3531070afd256661a6fbf522e78fc669" data-mlang="latex" data-equation="%5Cfrac%7Bf(x)%7D%7Bg(x)%7D%3Df(x)g%5E%7B-1%7D(x)"></picture>.</p>

MATH 2163 Lecture 13: Product and chain rule

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