Quotient Rule
{g(x)f'(x)-f(x)g'(x)}/g(x)^2
The quotient rule is a rule used in calculus to find the derivative of a quotient of two functions. If we have two functions f(x) and g(x), then the quotient rule states that the derivative of their quotient f(x)/g(x) is:
[f'(x) * g(x) – g'(x) * f(x)] / [g(x)]^2
In simpler terms, this means that we take the derivative of the numerator and multiply it by the denominator, then subtract the derivative of the denominator times the numerator and divide the whole thing by the square of the denominator.
It is important to note that we can only use the quotient rule when g(x) is not equal to zero. This is because if g(x) is equal to zero, then the denominator of the quotient becomes zero, and the whole expression becomes undefined.
The quotient rule is particularly useful when we are trying to find the derivative of a complex function that can be expressed as a quotient of two simpler functions. By using the quotient rule, we can simplify the process of finding the derivative of the complex function.
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