Understanding the Quotient Rule in Calculus | Differentiating Complex Functions Involving Ratios

quotient rule

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

The quotient rule is a formula used in calculus to differentiate a function that is the ratio of two other functions. It provides a method to find the derivative of a quotient of two functions.

The quotient rule states that if we have a function, denoted as f(x), which is the ratio of two other functions, say g(x) and h(x), then the derivative of f(x) can be found using the following formula:

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

Breaking down the formula, we have:

1. Find the derivative of the numerator, g'(x).
2. Multiply g'(x) by h(x).
3. Find the derivative of the denominator, h'(x).
4. Multiply g(x) by h'(x).
5. Subtract the result from step 4 from the result of step 2.
6. Divide the result from step 5 by [h(x)]^2.

By using the quotient rule, we can differentiate functions that involve divisions and fractions. It is a useful tool in calculus to find the derivative of complex functions or functions that cannot be easily differentiated using basic derivative rules like the power rule or product rule.

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