Quotient rule
(f’g-g’f)/g^2
The quotient rule is a formula used to find the derivative of a function that is the quotient of two other functions. It states that if f(x) and g(x) are two differentiable functions, then the derivative of their quotient, f(x)/g(x), is given by:
(f(x)/g(x))’ = (f'(x)g(x) – g'(x)f(x)) / [g(x)]^2
In simpler terms, to find the derivative of the quotient of two functions, you need to take the derivative of the numerator, multiply it by the denominator, subtract the derivative of the denominator multiplied by the numerator, and then divide the result by the denominator squared.
It is important to note that the quotient rule only works for functions where the denominator is not equal to zero. If the denominator is equal to zero, then the derivative does not exist. Additionally, the quotient rule can also be extended to cases where both the numerator and denominator are functions of another variable, such as y=f(x)/g(x), where both y and x are variables.
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