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In calculus, the quotient rule is a method of finding the derivative of a function that is the ratio of two differentiable functions. Let () = () ...
2.3 The quotient rule. ... The derivative of the function at a point is the slope of the line tangent to the curve ... Differential of a function – Notion in calculus;
Sum rule in differentiation; Constant factor rule in differentiation; Linearity of differentiation; Power rule; Chain rule; Local linearization; Product rule; Quotient rule; Inverse functions and differentiation; Implicit differentiation; Stationary point. Maxima and minima; First derivative test; Second derivative test; Extreme value theorem ...
The symmetric difference quotient is employed as the method of approximating the derivative in a number of calculators, including TI-82, TI-83, TI-84, TI-85, all of which use this method with h = 0.001. [2] [3]
In these limits, the infinitesimal change is often denoted or .If () is differentiable at , (+) = ′ ().This is the definition of the derivative.All differentiation rules can also be reframed as rules involving limits.
The study of differential calculus is unified with the calculus of finite differences in time scale calculus. [54] The arithmetic derivative involves the function that is defined for the integers by the prime factorization. This is an analogy with the product rule. [55]
The validity of this rule follows from the validity of the Feynman method, for one may always substitute a subscripted del and then immediately drop the subscript under the condition of the rule. For example, from the identity A ⋅( B × C ) = ( A × B )⋅ C we may derive A ⋅(∇× C ) = ( A ×∇)⋅ C but not ∇⋅( B × C ) = (∇× B ...
The theorem is a generalization of the second fundamental theorem of calculus to any curve in a plane or space (generally n-dimensional) rather than just the real line. If φ : U ⊆ R n → R is a differentiable function and γ a differentiable curve in U which starts at a point p and ends at a point q, then