Quotient Rule
The quotient rule is a formula used to find the derivative of a quotient of two functions
The quotient rule is a formula used to find the derivative of a quotient of two functions. It is particularly useful when differentiating rational functions.
The quotient rule states that if you have a function f(x) divided by another function g(x), then the derivative of this quotient is given by:
(f'(x) * g(x) – f(x) * g'(x)) / (g(x))^2
In other words, to find the derivative of a quotient, you take the derivative of the numerator (f'(x)), multiply it by the denominator (g(x)), subtract the product of the numerator (f(x)) and the derivative of the denominator (g'(x)), and then divide the whole expression by the square of the denominator (g(x))^2.
This rule is derived from the product rule and allows us to differentiate any quotient of two functions, regardless of their complexity. It is particularly useful when dealing with rational functions, which are functions in the form of a polynomial divided by another polynomial.
By using the quotient rule, we can find the derivative of functions like f(x) = (3x^2 + 2) / (x^3 – 4x). We would differentiate the numerator and denominator separately, apply the quotient rule formula, and simplify the expression to get the derivative of the function.
It’s important to note that the quotient rule is only applicable when the denominator is not equal to zero, as division by zero is undefined. So, before using the quotient rule, it’s necessary to ensure that the denominator of the function is not equal to zero.
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