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  2. Derivative - Wikipedia

    en.wikipedia.org/wiki/Derivative

    In mathematics, the derivative is a fundamental tool that quantifies the sensitivity to change of a function's output with respect to its input. 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.

  3. 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

  4. Numerical differentiation - Wikipedia

    en.wikipedia.org/wiki/Numerical_differentiation

    A simple two-point estimation is to compute the slope of a nearby secant line through the points (x, f(x)) and (x + h, f(x + h)). [1] Choosing a small number h , h represents a small change in x , and it can be either positive or negative.

  5. Xcas - Wikipedia

    en.wikipedia.org/wiki/Xcas

    Xcas has the ability of a scientific calculator that provides ... plot(3 * x^2 - 5) produces a plot of y = 3x 2 − 5; ... (the derivatives are written as y ...

  6. Third derivative - Wikipedia

    en.wikipedia.org/wiki/Third_derivative

    In calculus, a branch of mathematics, the third derivative or third-order derivative is the rate at which the second derivative, or the rate of change of the rate of change, is changing. The third derivative of a function y = f ( x ) {\displaystyle y=f(x)} can be denoted by

  7. Differentiation rules - Wikipedia

    en.wikipedia.org/wiki/Differentiation_rules

    The derivative of the function at a point is the slope of the line tangent to the curve at the point. Slope of the constant function is zero, because the tangent line to the constant function is horizontal and its angle is zero. In other words, the value of the constant function, y, will not change as the value of x increases or decreases.

  8. 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.

  9. Differential (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Differential_(mathematics)

    Using calculus, it is possible to relate the infinitely small changes of various variables to each other mathematically using derivatives. If y is a function of x, then the differential dy of y is related to dx by the formula =, where denotes not 'dy divided by dx' as one would intuitively read, but 'the derivative of y with respect to x '.