Calculus I - Derivatives of Exponential and Logarithm Functions

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Section 3.6 : Derivatives of Exponential and Logarithm Functions

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3. Differentiate \(R\left( w \right) = {3^w}\log \left( w \right)\) .

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Not much to do here other than take the derivative using the formulas from class. \[\require{bbox} \bbox[2pt,border:1px solid black]{{R'\left( w \right) = {3^w}\ln \left( 3 \right)\log \left( w \right) + \frac{{{3^w}}}{{w\ln \left( {10} \right)}}}}\]

Recall that \(\log \left( x \right)\) is the common logarithm and so is really \({\log _{10}}\left( x \right)\).