Derivative Operators

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Returns the first derivative of f(t) with respect to t, and evaluated at the point t.

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Returns the nth derivative of f(t) with respect to t, and evaluated at the point t. The numerical method used is a variation on Ridder's method, which calculates (n + 1)-point divided differences using a variety of step sizes, then uses weighted averages to compute successive approximations in a table. Successive table entries are compared, and the one with the smallest error is returned as the derivative, if the error is below some acceptable level. You can expect the first derivative to be accurate to within 7 or 8 significant digits, provided that the value at which you evaluate the derivative is not too close to a singularity of the function. Accuracy tends to decrease by one significant digit for each increase in the order of the derivative.

Operands:

• f(t) is a scalar valued function. f may be complex, and can be a function of any number of variables, as long as the other variables are previously defined.
• t is the previously defined point at which the derivative is to be evaluated.
• n is an integer between 0 and 5.

Example:

Notes:

• Although the nth derivative operator won't compute derivatives of order greater than 5, you can nest derivative operators within each other to compute higher order derivatives, with associated loss in accuracy for each successive order.
• You can change the display of these operators to a partial derivative symbol.
• If f has several terms, be sure to enclose them in parentheses to keep them inside the derivative operator.
• You can use this operator to differentiate symbolically.

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