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  2. Chain rule - Wikipedia

    en.wikipedia.org/wiki/Chain_rule

    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, ′ = ′ = (′) ′.

  3. Differentiation rules - Wikipedia

    en.wikipedia.org/wiki/Differentiation_rules

    The logarithmic derivative is another way of stating the rule for differentiating the logarithm of a function (using the chain rule): (⁡) ′ = ′ wherever f is positive. ...

  4. Total derivative - Wikipedia

    en.wikipedia.org/wiki/Total_derivative

    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

  5. Vector calculus identities - Wikipedia

    en.wikipedia.org/wiki/Vector_calculus_identities

    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 ...

  6. Quotient rule - Wikipedia

    en.wikipedia.org/wiki/Quotient_rule

    3.3 Proof using the reciprocal rule or chain rule. ... In calculus, the quotient rule is a method of finding the derivative of a function that is the ratio of two ...

  7. Faà di Bruno's formula - Wikipedia

    en.wikipedia.org/wiki/Faà_di_Bruno's_formula

    Faà di Bruno's formula is an identity in mathematics generalizing the chain rule to higher derivatives. It is named after Francesco Faà di Bruno (1855, 1857), although he was not the first to state or prove the formula.

  8. Leibniz's notation - Wikipedia

    en.wikipedia.org/wiki/Leibniz's_notation

    One reason that Leibniz's notations in calculus have endured so long is that they permit the easy recall of the appropriate formulas used for differentiation and integration. For instance, the chain rule—suppose that the function g is differentiable at x and y = f(u) is differentiable at u = g(x).

  9. Stratonovich integral - Wikipedia

    en.wikipedia.org/wiki/Stratonovich_integral

    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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