quotient rule
a^m/a^n = a^m-nWhen dividing 2 like bases, subtract exponents
The quotient rule is a formula used to find the derivative of a function that can be expressed as the quotient of two other functions. The formula is as follows:
If f(x) and g(x) are differentiable functions, then:
(f/g)’ = [g * f’ – f * g’] / g^2
In words, this formula states that the derivative of f(x)/g(x) is equal to the numerator (g(x) times the derivative of f(x) minus f(x) times the derivative of g(x)) divided by the denominator squared.
The quotient rule is also sometimes written in a different form, which is algebraically equivalent to the first:
(f/g)’ = (g * f’ – f * g’) / g^2
To use the quotient rule to find the derivative of a function, identify f(x) and g(x) and then apply the formula. Be sure to simplify the expression after differentiating it to get the final result.
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