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Chapter 13: Problem 33

What is the quota rule?

Short Answer

Expert verified
The quota rule, also called the quotient rule, is a method for finding the derivative of a function that is a ratio of two differentiable functions. It is given by the formula: \( h'(x) = \frac{f'(x)g(x) - f(x)g'(x)}{[g(x)]^2} \) where \( h(x) = \frac{f(x)}{g(x)} \), and both f and g are differentiable.

Step by step solution

01

Define the Quota Rule

The Quota Rule, also known as the quotient rule is a method to find the derivative of a function that is a ratio of two differentiable functions. It provides a formula to find the derivative of complex fractions. The formula is stated as: If you have a function that is divided by another function i.e. \( h(x) = \frac{f(x)}{g(x)} \) where both f and g are differentiable, then the derivative \( h'(x) \) can be found as \( h'(x) = \frac{f'(x)g(x) - f(x)g'(x)}{[g(x)]^2} \).

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Most popular questions from this chapter

Three candidates, \(\mathrm{A}, \mathrm{B}\), and \(\mathrm{C}\), are running for mayor. Election rules stipulate that the plurality method will determine the winner. In the event that the plurality method leads to a tie, the Borda count method will decide the winner. The election results are summarized in the following preference table. Under these rules, which candidate becomes the new mayor? $$ \begin{array}{|l|c|c|c|} \hline \text { Number of Votes } & \mathbf{1 2 , 0 0 0} & \mathbf{7 5 0 0} & \mathbf{4 5 0 0} \\ \hline \text { First Choice } & \text { C } & \text { A } & \text { A } \\ \hline \text { Second Choice } & \text { B } & \text { B } & \text { C } \\ \hline \text { Third Choice } & \text { A } & \text { C } & \text { B } \\ \hline \end{array} $$

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