Built-in Functions and Constants

This topic provides help on Derive’s built-in mathematical functions and constants. Utility Function FilesG5BS2R describes the numerous functions defined in the utility files distributed with Derive. Author > Function Definition command1ER8JVI and Programming in DERIVEProgramming describe how to define your own functions in terms of Derive 's built-in operators, functions, and constants.

Numerous automatic and some optional transformations are used to simplify expressions involving the built-in functions and constants. To see a demonstration of these simplifications, load the files TRIG.DMO and FUNCTION.DMO using a File > Load File > Demo File command11YMWXT.

Note that these transformations are not applied to an expression until you issue a Simplify commandSimplify_commands. Merely entering an expression is not sufficient to force simplification, unless you click on the Simplify button to issue the Author commands.

Some transformations for simplifying the built-in functions are valid only for a restricted domain of values. For example, it is not valid to simplify LN(x^2)/2 to LN(x) if x is negative.

When simplifying an expression, Derive does not exploit a transformation unless it can determine that the transformation is valid. This determination depends on the domain of the variables in the expression. Use the Author > Variable Domain command8MNT4Y to restrict the domain of variables so that more transformations can be applied.

Given numeric arguments, the value of most built-in functions is usually an irrational number which therefore cannot be computed exactly. For example, the square root of most rational numbers is irrational. So in exact mode, only certain special numeric arguments simplify to rational numbers. For example, in exact mode SQRT(4/9) simplifies to 2/3, but SQRT(8/9) simplifies to 2·SQRT(2)/3. You can use the Simplify Approximate command1LCSBCN to temporarily change the precision to obtain an approximate result.

Given a complex argument in rectangular form (see the Branch fieldBranch_field of the Options > Mode Settings > Simplification command19_L5FP), most built-in functions produce a simplified result that is also in rectangular form. For example, SQRT(3 - 4·#i) simplifies to 2 - #i.

Exponential FunctionsExponential_Functions

Logarithmic FunctionsLogarithmic_Functions

Trigonometric FunctionsTrigonometric_Functions

Inverse Trigonometric FunctionsInverse_Trigonometric_Functions

Hyperbolic FunctionsHyperbolic_Functions

Inverse Hyperbolic FunctionsInverse_Hyperbolic_Functions

Piecewise Continuous FunctionsPiecewise_Continuous_Functions

Complex Variable FunctionsComplex_Variable_Functions

Probability FunctionsProbability_Functions

Statistical FunctionsStatistical_Functions

Error FunctionsError_Functions

Zeta FunctionsZeta_Functions