Section 3.4 : Product and Quotient Rule
5. Use the Quotient Rule to find the derivative of \(\displaystyle R\left( w \right) = \frac{{3w + {w^4}}}{{2{w^2} + 1}}\) .
Show SolutionThere isn’t much to do here other than take the derivative using the quotient rule.
\[R'\left( w \right) = \frac{{\left( {3 + 4{w^3}} \right)\left( {2{w^2} + 1} \right) - \left( {3w + {w^4}} \right)\left( {4w} \right)}}{{{{\left( {2{w^2} + 1} \right)}^2}}} = \require{bbox} \bbox[2pt,border:1px solid black]{{\frac{{4{w^5} + 4{w^3} - 6{w^2} + 3}}{{{{\left( {2{w^2} + 1} \right)}^2}}}}}\]