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  2. Derivative - Wikipedia

    en.wikipedia.org/wiki/Derivative

    Another common notation for differentiation is by using the prime mark in the symbol of a function ⁠ ⁠. This is known as prime notation , due to Joseph-Louis Lagrange . [ 22 ] The first derivative is written as ⁠ f ′ ( x ) {\displaystyle f'(x)} ⁠ , read as " ⁠ f {\displaystyle f} ⁠ prime of ⁠ x {\displaystyle x} ⁠ , or ⁠ y ...

  3. Differential of a function - Wikipedia

    en.wikipedia.org/wiki/Differential_of_a_function

    The differential was first introduced via an intuitive or heuristic definition by Isaac Newton and furthered by Gottfried Leibniz, who thought of the differential dy as an infinitely small (or infinitesimal) change in the value y of the function, corresponding to an infinitely small change dx in the function's argument x.

  4. Differentiation rules - Wikipedia

    en.wikipedia.org/wiki/Differentiation_rules

    Logarithmic differentiation is a technique which uses logarithms and its differentiation rules to simplify certain expressions before actually applying the derivative. [ citation needed ] Logarithms can be used to remove exponents, convert products into sums, and convert division into subtraction — each of which may lead to a simplified ...

  5. Notation for differentiation - Wikipedia

    en.wikipedia.org/wiki/Notation_for_differentiation

    Assume that (x, y, z) is a given Cartesian coordinate system, that A is a vector field with components = (,,), and that = (,,) is a scalar field. The differential operator introduced by William Rowan Hamilton , written ∇ and called del or nabla, is symbolically defined in the form of a vector,

  6. Differential calculus - Wikipedia

    en.wikipedia.org/wiki/Differential_calculus

    When x and y are real variables, the derivative of f at x is the slope of the tangent line to the graph of f at x. Because the source and target of f are one-dimensional, the derivative of f is a real number. If x and y are vectors, then the best linear approximation to the graph of f depends on how f changes in several

  7. Leibniz's notation - Wikipedia

    en.wikipedia.org/wiki/Leibniz's_notation

    Gottfried Wilhelm von Leibniz (1646–1716), German philosopher, mathematician, and namesake of this widely used mathematical notation in calculus.. In calculus, Leibniz's notation, named in honor of the 17th-century German philosopher and mathematician Gottfried Wilhelm Leibniz, uses the symbols dx and dy to represent infinitely small (or infinitesimal) increments of x and y, respectively ...

  8. Differential equation - Wikipedia

    en.wikipedia.org/wiki/Differential_equation

    In all these cases, y is an unknown function of x (or of x 1 and x 2), and f is a given function. He solves these examples and others using infinite series and discusses the non-uniqueness of solutions. Jacob Bernoulli proposed the Bernoulli differential equation in 1695. [3] This is an ordinary differential equation of the form

  9. Differentiation of trigonometric functions - Wikipedia

    en.wikipedia.org/wiki/Differentiation_of...

    Using implicit differentiation and then solving for dy/dx, the derivative of the inverse function is found in terms of y. To convert dy/dx back into being in terms of x, we can draw a reference triangle on the unit circle, letting θ be y.