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The Quotient Rule in Words The Quotient Rule says that the derivative of a quotient is the denominator times the derivative of the numerator minus the numerator times the derivative of the denominator, all divided by the square of the denominator. Period____. Date________________. Differentiation - Quotient Rule. Differentiate each function with respect to x. 1) y = 2. 2x. 4 ? 5. 2) f (x) = 2 x. 5 ? 5. 3) f (x) =. Instead, the rule for finding the derivative of a product is as follows: Product rule. For functions f and g, d dx. [f(x)g(x)] =. Jun 1, 2004 - df dx. = (6x2 + 2x)(3x2)+(x3 + 1)(12x + 2),. = 18x4 + 6x3 + 12x4 + 2x3 + 12x + 2,. = 30x4 + 8x3 + 12x + 2. Rule 6: The Quotient Rule. The derivative of the quotient f( Differentiation: Quotient Rule. The Quotient Rule is used when we want to differentiate a function that may be regarded as a quotient of two simpler functions. The quotient rule tells us that if u(x) and v(x) are differentiable functions, The derivative of sin(x) is cos(x) and the derivative of x is 1, so the quotient rule tells us A special rule, the quotient rule, exists for differentiating quotients of two There is a formula we can use to differentiate a quotient - it is called the quotient rule. A special rule, the quotient rule, exists for differentiating quotients of two There is a formula we can use to differentiate a quotient - it is called the quotient rule. The rule states: Key Point. The quotient rule: if y = u v then dy dx. = vdu dx ? udv dx v2. Let's see how the formula works when we try to differentiate y = cosx x2.