The formula for finding the derivative of a quotient with the same variables on the top and bottom is (f'(x)g(x) - f(x)g'(x))/[g(x)]^2, where f(x) and g(x) are the numerator and denominator functions, respectively.
The power rule for finding the derivative of a quotient with the same variables on the top and bottom is to differentiate the numerator and denominator separately, and then divide the two derivatives. For example, if the quotient is (x^2 + 2x + 3)/(x^2 + 1), the derivative would be [(2x + 2)(x^2 + 1) - (x^2 + 2x + 3)(2x)]/(x^2 + 1)^2.
The general rule for finding the derivative of a quotient with the same variables on the top and bottom is to use the quotient rule, which is (f'(x)g(x) - f(x)g'(x))/[g(x)]^2, where f(x) and g(x) are the numerator and denominator functions, respectively.
Yes, the quotient rule can be applied to any quotient with the same variables on the top and bottom, regardless of the complexity of the functions. However, it may be easier to use other derivative rules, such as the power rule or product rule, in some cases.
The quotient rule differs from the power rule and product rule in that it specifically deals with finding the derivative of a quotient, while the power rule and product rule deal with finding the derivative of a single function or the product of two functions, respectively. The quotient rule also involves subtracting the product of the derivatives of the numerator and denominator, while the other rules involve adding or multiplying the derivatives of the individual functions.