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  2. 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 is positive. Logarithmic differentiation is a technique which uses logarithms and its differentiation rules to simplify certain expressions before actually applying the derivative.

  3. Euler method - Wikipedia

    en.wikipedia.org/wiki/Euler_method

    The next step is to multiply the above value by the step size , which we take equal to one here: h ⋅ f ( y 0 ) = 1 ⋅ 1 = 1. {\displaystyle h\cdot f(y_{0})=1\cdot 1=1.} Since the step size is the change in t {\displaystyle t} , when we multiply the step size and the slope of the tangent, we get a change in y {\displaystyle y} value.

  4. Fourth, fifth, and sixth derivatives of position - Wikipedia

    en.wikipedia.org/wiki/Fourth,_fifth,_and_sixth...

    The higher-order derivatives are less common than the first three; [1] [2] thus their names are not as standardized, though the concept of a minimum snap trajectory has been used in robotics. [ 3 ] The fourth derivative is referred to as snap , leading the fifth and sixth derivatives to be "sometimes somewhat facetiously" [ 4 ] called crackle ...

  5. Five-point stencil - Wikipedia

    en.wikipedia.org/wiki/Five-point_stencil

    An illustration of the five-point stencil in one and two dimensions (top, and bottom, respectively). In numerical analysis, given a square grid in one or two dimensions, the five-point stencil of a point in the grid is a stencil made up of the point itself together with its four "neighbors".

  6. Derivative - Wikipedia

    en.wikipedia.org/wiki/Derivative

    The derivative of the function given by () = + ⁡ ⁡ + is ′ = + ⁡ (⁡) ⁡ () + = + ⁡ ⁡ (). Here the second term was computed using the chain rule and the third term using the product rule. The known derivatives of the elementary functions , , ⁡ (), ⁡ (), and ⁡ =, as well as the constant , were also used.

  7. Differential calculus - Wikipedia

    en.wikipedia.org/wiki/Differential_calculus

    [4] [d] We have thus succeeded in properly defining the derivative of a function, meaning that the 'slope of the tangent line' now has a precise mathematical meaning. Differentiating a function using the above definition is known as differentiation from first principles.

  8. Finite difference coefficient - Wikipedia

    en.wikipedia.org/wiki/Finite_difference_coefficient

    The theory of Lagrange polynomials provides explicit formulas for the finite difference coefficients. [4] For the first six derivatives we have the following: Derivative

  9. Product rule - Wikipedia

    en.wikipedia.org/wiki/Product_rule

    In calculus, the product rule (or Leibniz rule [1] or Leibniz product rule) is a formula used to find the derivatives of products of two or more functions.For two functions, it may be stated in Lagrange's notation as () ′ = ′ + ′ or in Leibniz's notation as () = +.