The Quotient Rule | Calculating Derivatives of Quotient Functions in Calculus

Quotient Rule

The quotient rule is a formula used in calculus to find the derivative of a function that is a quotient of two other functions

The quotient rule is a formula used in calculus to find the derivative of a function that is a quotient of two other functions. It is particularly useful when you have a function that can be written as the ratio of two functions.

The quotient rule states that if you have a function f(x) that can be written as f(x) = g(x) / h(x), where g(x) and h(x) are both differentiable functions, then the derivative of f(x), denoted as f'(x), is given by:

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

In simpler terms, to find the derivative of a quotient of two functions, you need to follow these steps:

1. Differentiate the numerator function, g(x), to get g'(x).
2. Differentiate the denominator function, h(x), to get h'(x).
3. Multiply g'(x) with h(x).
4. Multiply g(x) with h'(x).
5. Subtract the results obtained in steps 3 and 4.
6. Divide the result obtained in step 5 by (h(x))^2 to get the final derivative f'(x).

It is important to note that the denominator function, h(x), should not be equal to zero in the given interval, as division by zero is undefined.

The quotient rule is a helpful tool when dealing with functions that involve division, such as rational functions or functions that are ratios of polynomials. By using the quotient rule, you can find the derivative of these functions and analyze their slopes, rates of change, or other properties.

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