Derivative
 Usage
• f' represents the derivative of a function f of one argument.
• 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.
Notes
• f' is equivalent to Derivative[1][f]. • f'' evaluates to Derivative[2][f]. • You can think of Derivative as a functional operator which acts on functions to give derivative functions. • Derivative is generated when you apply D to functions whose derivatives Mathematica does not know. • 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. • Example: Cos'  . • Derivative[-n][f] represents the n indefinite integral of f. • 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. • N[f'[x]] will give a numerical approximation to a derivative. • New in Version 1; modified in 4.
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