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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. Chain rule (probability) - Wikipedia

    en.wikipedia.org/wiki/Chain_rule_(probability)

    This rule allows one to express a joint probability in terms of only conditional probabilities. [4] The rule is notably used in the context of discrete stochastic processes and in applications, e.g. the study of Bayesian networks, which describe a probability distribution in terms of conditional probabilities.

  4. Chain rule of probability - Wikipedia

    en.wikipedia.org/?title=Chain_rule_of...

    Download as PDF; Printable version; From Wikipedia, the free encyclopedia ... Retrieved from " ...

  5. Parametric derivative - Wikipedia

    en.wikipedia.org/wiki/Parametric_derivative

    This can be derived using the chain rule for derivatives: = and dividing both sides by to give the equation above. In general all of these derivatives — dy / dt , dx / dt , and dy / dx — are themselves functions of t and so can be written more explicitly as, for example, d y d x ( t ) {\displaystyle {\frac {dy}{dx}}(t)} .

  6. Chain rule for Kolmogorov complexity - Wikipedia

    en.wikipedia.org/wiki/Chain_rule_for_Kolmogorov...

    The chain rule [citation needed] for Kolmogorov complexity is an analogue of the chain rule for information entropy, which states: (,) = + (|) That is, the combined randomness of two sequences X and Y is the sum of the randomness of X plus whatever randomness is left in Y once we know X.

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  8. 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.

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