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FilledSmallSquare f' represents the derivative of a function f of one argument.

FilledSmallSquare Derivative[, , ... ][f] is the general form, representing a function obtained from f by differentiating times with respect to the first argument, times with respect to the second argument, and so on.

FilledSmallSquare f' is equivalent to Derivative[1][f].

FilledSmallSquare f'' evaluates to Derivative[2][f].

FilledSmallSquare You can think of Derivative as a functional operator which acts on functions to give derivative functions.

FilledSmallSquare Derivative is generated when you apply D to functions whose derivatives Mathematica does not know.

FilledSmallSquare Mathematica attempts to convert Derivative[n][f] and so on to pure functions. Whenever Derivative[n][f] is generated, Mathematica rewrites it as D[f[#]&, #, n]. If Mathematica finds an explicit value for this derivative, it returns this value. Otherwise, it returns the original Derivative form.

FilledSmallSquare Example: Cos' LongRightArrow.

FilledSmallSquare Derivative[-n][f] represents the n indefinite integral of f.

FilledSmallSquare Derivative[, , ... ][f] represents the derivative of f[, , ... ] taken times with respect to . In general, arguments given in lists in f can be handled by using a corresponding list structure in Derivative.

FilledSmallSquare N[f'[x]] will give a numerical approximation to a derivative.

FilledSmallSquare See Section 2.2.8 and Section 3.5.4.

FilledSmallSquare See also: D, Dt.

FilledSmallSquare New in Version 1; modified in 4.0.

Further Examples