The Quotient Rule

Business Calculus · Axiom Academy

Differentiating fractions of functions When Division Gets Complicated We've learned the product rule for f g . What about quotients like g ? Consider the function h(x) = x - 3 . We can't simplify this, and we can't use the power rule directly. The derivative of a quotient is NOT the quotient of the derivatives! We need a special rule for handling division of functions. If f and g are differentiable and g(x) 0 , then: (bottom × derivative of top − top × derivative of bottom) ÷ bottom² Find the derivative of h(x) = x - 3 Apply: "Lo d-Hi minus Hi d-Lo over Lo-Lo" Find the derivative of y = x^2 + 1 The numerator often simplifies nicely! Always expand and combine like terms before declaring your final answer. Click each problem to reveal the solution: Simple quotients like x^2 can be rewritten as x^ -2 and differentiated with the power rule. Often easier! Find the derivative of f(x) = x + 2 You've mastered the Quotient Rule! "Lo d-Hi minus Hi d-Lo, over Lo-Lo" Next up: The Chain Rule for composite functions!

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