The Calc Library

Derivatives

The Execute command is used to evaluate derivatives. Examples include expressions like:

Note that some basic simplification is done on derivatives but they are not necessarily simplified all the way to their simplest form.

The Expand command can be used to evaluate derivatives one step at a time. For example, you get the right-hand side of this expression by applying the Expand command to the left-hand side:

which is just an application of the general rule for derivatives of products:

Basic Integrals

The Execute command is also used to evaluate integrals. Examples include expressions like:

Constants and numeric values can be pull out in front of an integral using the Simplify command.

Integration by Parts

The Execute command on an integral will test to see if the integral has a form that allows evaluation using integration by parts. In addition, you can control how integration by parts is applied to an integral by moving terms into the differential before using the Execute command. For example, if you have the integral:

you can highlight the e^x term, press Shift + Right arrow to also highlight the dx term and then use the Equivalence command to get:

Now you can use the Execute command to get:

The Equivalence command can also be used on

It just does a direct application of:

Constants

Constants (for purposes of integration and differentiation) can be created using the Constant declaration. See Declaration Objects for more details.