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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 chain rule has a particularly elegant statement in terms of total derivatives. It says that, for two functions f {\displaystyle f} and g {\displaystyle g} , the total derivative of the composite function f ∘ g {\displaystyle f\circ g} at a {\displaystyle a} satisfies
Download as PDF; Printable version; ... or from the combination of power rule and chain rule. The quotient rule ... both on elementary and advanced calculus, in pure ...
Chain rule – For derivatives of composed functions; Differentiation of trigonometric functions – Mathematical process of finding the derivative of a trigonometric function; Differentiation rules – Rules for computing derivatives of functions; General Leibniz rule – Generalization of the product rule in calculus
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.
Calculus is the mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithmetic operations. Originally called infinitesimal calculus or "the calculus of infinitesimals", it has two major branches, differential calculus and integral calculus.
chain rule The chain rule is a formula for computing the derivative of the composition of two or more functions. That is, if f and g are functions, then the chain rule expresses the derivative of their composition f ∘ g (the function which maps x to f(g(x)) ) in terms of the derivatives of f and g and the product of functions as follows:
Because the Stratonovich calculus satisfies the ordinary chain rule, stochastic differential equations (SDEs) in the Stratonovich sense are more straightforward to define on differentiable manifolds, rather than just on . The tricky chain rule of the Itô calculus makes it a more awkward choice for manifolds.
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