• lemma
  • The lemma asserts that the existence of this derivative implies the existence of a function φ {\displaystyle \varphi } such that lim h → 0 φ ( h ) = 0 and f ( a + h ) = f ( a ) + f ′ ( a ) h + φ ( h ) h {\displaystyle \lim _{h\to 0}\varphi (h)=0\qquad {\text{and}}\qquad f(a+h)=f(a)+f'(a)h+\varphi (h)h} for sufficiently small but non-zero h. (wikipedia.org)
  • Bihari I., A generalization of a lemma of Bellman and its application to uniqueness problems of differential equations, Acta Math. (degruyter.com)
  • Lagrange's
  • In Lagrange's notation, the derivative with respect to x of a function f(x) is denoted f'(x) (read as "f prime of x") or fx′(x) (read as "f prime x of x"), in case of ambiguity of the variable implied by the derivation. (wikipedia.org)
  • partial
  • Each entry of this matrix represents a partial derivative, specifying the rate of change of one range coordinate with respect to a change in a domain coordinate. (wikipedia.org)
  • In patients misery from epilepsy, the Lyrical preparation is habituated to as a means of additional therapy after feeling an attraction (fond of) seizures, including partial seizures, which are accompanied aside inferior generalization. (dclans.ru)
  • In patients misery from epilepsy, the Lyrical preparation is occupied as a means of additional cure for feeling an attraction (partial) seizures, including incomplete seizures, which are accompanied by derivative generalization. (dclans.ru)
  • tangent
  • The derivative of a function of a single variable at a chosen input value, when it exists, is the slope of the tangent line to the graph of the function at that point. (wikipedia.org)
  • notation
  • f(a) then there exist a point z in (a, b) where the symmetric derivative is non-negative, or with the notation used above, fs(z) ≥ 0. (wikipedia.org)
  • slope
  • If x and y are real numbers, and if the graph of f is plotted against x, the derivative is the slope of this graph at each point. (wikipedia.org)
  • equation
  • A. Atangana and R. T. Alqahtani , Numerical approximation of the space-time Caputo-Fabrizio fractional derivative and application to groundwater pollution equation, Advances in Difference Equations , 2016 (2016), 1-13. (aimsciences.org)
  • velocity
  • In continuum mechanics, the material derivative describes the time rate of change of some physical quantity (like heat or momentum) of a material element that is subjected to a space-and-time-dependent macroscopic velocity field variations of that physical quantity. (wikipedia.org)
  • For example, the derivative of the position of a moving object with respect to time is the object's velocity: this measures how quickly the position of the object changes when time advances. (wikipedia.org)
  • dependent variable
  • For this reason, the derivative is often described as the "instantaneous rate of change", the ratio of the instantaneous change in the dependent variable to that of the independent variable. (wikipedia.org)
  • 2016
  • O. J. J. Algahtani , Comparing the Atangana-Baleanu and Caputo-Fabrizio derivative with fractional order: Allen Cahn model, Chaos Solitons and Fractals , 89 (2016), 552-559. (aimsciences.org)
  • B. S. T. Alkahtani , Chua's circuit model with Atangana-Baleanu derivative with fractional order, Chaos, Solitons and Fractals , 89 (2016), 547-551. (aimsciences.org)
  • B. S. T. Alkahtani and A. Atangana , Controlling the wave movement on the surface of shallow water with the Caputo-Fabrizio derivative with fractional order, Chaos Soliton and Fractals , 89 (2016), 539-546. (aimsciences.org)
  • A. Atangana and B. S. T. Alkahtani , New model of groundwater owing within a confine aquifer: Application of Caputo-Fabrizio derivative, Arabian Journal of Geosciences , 9 (2016), 3647-3654. (aimsciences.org)
  • commonly
  • No. 3,393,197 issued to Pachter and Matossian on July 16, 1968 disclose N-substituted-14-hydroxydihydronormorphines, including the N-cyclobutylmethyl derivative, commonly called nalbuphine. (google.com)
  • temperature
  • In which case, the material derivative then describes the temperature change of a certain fluid parcel with time, as it flows along its pathline (trajectory). (wikipedia.org)
  • linear
  • In this generalization, the derivative is reinterpreted as a linear transformation whose graph is (after an appropriate translation) the best linear approximation to the graph of the original function. (wikipedia.org)
  • value
  • Its value is then the derivative ƒ'(x). (wikipedia.org)
  • The derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value). (wikipedia.org)
  • The derivative of a function y = f(x) of a variable x is a measure of the rate at which the value y of the function changes with respect to the change of the variable x. (wikipedia.org)