Operators > Calculus Operators > Derivative and Prime Operators
Derivative and Prime Operators
Operator
Description
Keyboard Shortcut
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.
Ctrl+Shift+D
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.
Ctrl+D
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.
Ctrl+' (Apostrophe)
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.
Was this helpful?