Derivative and Prime Operators
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Operator
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Description
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Keyboard Shortcut
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Returns the nth derivative of f(t) with respect to t, and evaluated at point t.
• For numeric evaluation, n is a natural number between 0 and 5, inclusive.
• For symbolic evaluation, n can be any natural number.
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Ctrl+Shift+D
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Returns the nth partial derivative of f(t) with respect to t, and evaluated at point t.
• For numeric evaluation, n is a natural number between 0 and 5, inclusive.
• For symbolic evaluation, n can be any natural number.
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Ctrl+D
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Defines function g to be the 1st derivative of function f(t).
• You can cascade n prime operators to get the nth derivative.
• For numeric or symbolic evaluation you can have any number of prime operators. However, the symbolic evaluation calculation time is much faster.
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Ctrl+' (Apostrophe)
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Operands
• f(t) is a scalar-valued function. The function can be complex.
◦ For the derivative operator, f(t) can be a function of any number of variables.
◦ For the prime operator, f(t) must be a function of one variable only.
• g is a function name.
• t is the point at which the derivative is evaluated.
Additional Information
• You can leave the exponent placeholder of the derivative operator empty when evaluating the first derivative of an expression.
• The first derivative is 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 about 1 significant digit for each increase in the order of the derivative.
• The numerical method used for calculating derivatives is a variation on Ridder's method, which calculates (n + 1) point divided differences using a variety of step sizes where n is the order of the derivative. It 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.