Quotient rule of f(x)/g(x)
g(x)f'(x)-f(x)g'(x)/g(x)²
The quotient rule is a derivative rule used to find the derivative of a function that has a quotient or fraction in the form of f(x)/g(x). The quotient rule states that:
The derivative of the quotient of two functions, f(x) and g(x), is equal to the numerator, f'(x), multiplied by the denominator, g(x), minus the numerator, f(x), multiplied by the denominator, g'(x), all divided by the square of the denominator, g(x)^2.
In mathematical notation, the quotient rule can be expressed as:
(f/g)'(x) = [f'(x)*g(x) – f(x)*g'(x)] / [g(x)^2]
This formula applies to any differentiable functions f(x) and g(x) with g(x) ≠ 0.
It is important to note that the numerator is the derivative of the function in the numerator and the denominator is the function in the denominator squared. Additionally, the quotient rule can be difficult to use in practice due to its complexity, so it may be useful to simplify the function prior to applying the rule if possible.
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