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  2. Derivative test - Wikipedia

    en.wikipedia.org/wiki/Derivative_test

    The higher-order derivative test or general derivative test is able to determine whether a function's critical points are maxima, minima, or points of inflection for a wider variety of functions than the second-order derivative test. As shown below, the second-derivative test is mathematically identical to the special case of n = 1 in the ...

  3. nth-term test - Wikipedia

    en.wikipedia.org/wiki/Nth-term_test

    Many authors do not name this test or give it a shorter name. [2] When testing if a series converges or diverges, this test is often checked first due to its ease of use. In the case of p-adic analysis the term test is a necessary and sufficient condition for convergence due to the non-Archimedean ultrametric triangle inequality.

  4. Power rule - Wikipedia

    en.wikipedia.org/wiki/Power_rule

    In addition, if is a positive integer, then there is no need for a branch cut: one may define () =, or define positive integral complex powers through complex multiplication, and show that ′ = for all complex , from the definition of the derivative and the binomial theorem.

  5. 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. ...

  6. Numerical differentiation - Wikipedia

    en.wikipedia.org/wiki/Numerical_differentiation

    Given below is the five-point method for the first derivative (five-point stencil in one dimension): [10] ′ = (+) + (+) + + (), where [, +]. For other stencil configurations and derivative orders, the Finite Difference Coefficients Calculator is a tool that can be used to generate derivative approximation methods for any stencil with any ...

  7. Maximum likelihood estimation - Wikipedia

    en.wikipedia.org/wiki/Maximum_likelihood_estimation

    If the likelihood function is differentiable, the derivative test for finding maxima can be applied. In some cases, the first-order conditions of the likelihood function can be solved analytically; for instance, the ordinary least squares estimator for a linear regression model maximizes the likelihood when the random errors are assumed to have ...

  8. Notation for differentiation - Wikipedia

    en.wikipedia.org/wiki/Notation_for_differentiation

    for the first derivative, for the second derivative, for the third derivative, and for the nth derivative. When f is a function of several variables, it is common to use "∂", a stylized cursive lower-case d, rather than "D". As above, the subscripts denote the derivatives that are being taken.

  9. Finite difference - Wikipedia

    en.wikipedia.org/wiki/Finite_difference

    In an analogous way, one can obtain finite difference approximations to higher order derivatives and differential operators. For example, by using the above central difference formula for f ′(x + ⁠ h / 2 ⁠) and f ′(x − ⁠ h / 2 ⁠) and applying a central difference formula for the derivative of f ′ at x, we obtain the central difference approximation of the second derivative of f: