Quotient rule

Formula for the derivative of a ratio of functions

In calculus, the quotient rule is a method of finding the derivative of a function that is the ratio of two differentiable functions. Let ⁠ h ( x) = f ( x) g ( x) {\displaystyle \textstyle h(x)={\frac {f(x)}{g(x)}}} ⁠, where both ⁠ f {\displaystyle f} ⁠ and ⁠ g {\displaystyle g} ⁠ are differentiable and ⁠ g ( x) ≠ 0 {\displaystyle g(x)\neq 0} ⁠. The quotient rule states that the derivative of ⁠ h ( x) {\displaystyle h(x)} ⁠ is h ′ ( x) = f ′ ( x) g ( x) − f ( x) g ′ ( x) ( g ( x)) 2 .

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