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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.
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.
Automatic differentiation is a subtle and central tool to automatize the simultaneous computation of the numerical values of arbitrarily complex functions and their derivatives with no need for the symbolic representation of the derivative, only the function rule or an algorithm thereof is required.
Here is a brief overview of what Xcas is able to do: [9] [10] Xcas has the ability of a scientific calculator that provides show input and writes pretty print; Xcas also works as a spreadsheet; [11]
The derivatives in the table above are for when the range of the inverse secant is [,] and when the range of the inverse cosecant is [,]. It is common to additionally define an inverse tangent function with two arguments , arctan ( y , x ) {\textstyle \arctan(y,x)} .
The calculus of variations (or variational calculus) is a field of mathematical analysis that uses variations, which are small changes in functions and functionals, to find maxima and minima of functionals: mappings from a set of functions to the real numbers.
Derive 1.0 - A Mathematical Assistant Program (2nd printing, 3rd ed.). Honolulu, Hawaii, USA: Soft Warehouse, Inc. August 1989 [June 1989 (September 1988)]. Jerry Glynn, Exploring Math from Algebra to Calculus with Derive, A Mathematical Assistant, Mathware Inc, 1992, ISBN 0-9623629-0-5
The primary reason for such advocacy is that computer algebra systems represent real-world math more than do paper-and-pencil or hand calculator based mathematics. [12] This push for increasing computer usage in mathematics classrooms has been supported by some boards of education. It has even been mandated in the curriculum of some regions. [13]