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The logarithmic derivative is another way of stating the rule for differentiating the logarithm of a function (using the chain rule): () ′ = ′, wherever is positive. Logarithmic differentiation is a technique which uses logarithms and its differentiation rules to simplify certain expressions before actually applying the derivative.
In mathematics, specifically in calculus and complex analysis, the logarithmic derivative of a function f is defined by the formula ′ where ′ is the derivative of f. [1] Intuitively, this is the infinitesimal relative change in f ; that is, the infinitesimal absolute change in f, namely f ′ , {\displaystyle f',} scaled by the current ...
In calculus, logarithmic differentiation or differentiation by taking logarithms is a method used to differentiate functions by employing the logarithmic derivative of a function f, [1] () ′ = ′ ′ = () ′.
In calculus, the chain rule is a formula that expresses the derivative of the composition of two differentiable functions f and g in terms of the derivatives of f and g.More precisely, if = is the function such that () = (()) for every x, then the chain rule is, in Lagrange's notation, ′ = ′ (()) ′ (). or, equivalently, ′ = ′ = (′) ′.
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 ...
Simplest rules Derivative of a constant; 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 ...
The course begins with an introduction to functions and limits, and goes on to explain derivatives. By the end of this course, the student will have learnt the fundamental theorem of calculus, chain rule, derivatives of transcendental functions, integration, and applications of all these in the real world. This course is followed by Calculus Two.
That is, the derivative of the area function A(x) exists and is equal to the original function f(x), so the area function is an antiderivative of the original function. Thus, the derivative of the integral of a function (the area) is the original function, so that derivative and integral are inverse operations which reverse each other. This is ...