Section 3.4 : Product and Quotient Rule
6. Use the Quotient Rule to find the derivative of \(\displaystyle f\left( x \right) = \frac{{\sqrt x + 2x}}{{7x - 4{x^2}}}\) .
Show SolutionThere isn’t much to do here other than take the derivative using the quotient rule.
\[f'\left( x \right) = \frac{{\left( {{\textstyle{1 \over 2}}{x^{ - \,\,\frac{1}{2}}} + 2} \right)\left( {7x - 4{x^2}} \right) - \left( {{x^{\frac{1}{2}}} + 2x} \right)\left( {7 - 8x} \right)}}{{{{\left( {7x - 4{x^2}} \right)}^2}}}\]