How to Use the Quotient Rule to Find the Derivative of a Function

Quotient Rule

The quotient rule is a rule used in calculus to find the derivative of a quotient of two functions

The quotient rule is a rule used in calculus to find the derivative of a quotient of two functions. It applies when you have a function of the form f(x) = g(x) / h(x), where g(x) and h(x) are differentiable functions.

To find the derivative of f(x) using the quotient rule, you can follow these steps:

1. Differentiate the numerator g(x) with respect to x and denote it as g'(x).
2. Differentiate the denominator h(x) with respect to x and denote it as h'(x).
3. Apply the quotient rule formula, which states that the derivative of f(x) is equal to (g'(x) * h(x) – g(x) * h'(x)) / (h(x))^2.

In mathematical notation, the quotient rule can be expressed as follows:

d/dx (g(x) / h(x)) = (g'(x) * h(x) – g(x) * h'(x)) / (h(x))^2

This rule is especially helpful when dealing with functions that involve fractions, as it allows us to find the derivative of the quotient without having to expand or simplify the expression manually.

It is important to note that the quotient rule only applies when the denominator h(x) is not equal to zero, as division by zero is undefined.

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