See SingleStepOverview for an introduction to the step-by-step functionality available in the Calculus1 package.

For each of the operations supported by the Calculus1 package (Diff, Int, and Limit), the package maintains an understood rules list, which is a list of rules for the operation that are automatically applied (after any explicit rule you specify) by a Rule call.  You can also apply only these understood rules by calling Rule with an empty index ([]), for example, $\mathrm{Rule}\left[\right]\left(\int \left(x^2+x\right)\ⅆx\right)$.

The Understand() command returns the current understood rules lists for each of the Calculus1 operations (Diff, Int, and Limit).

The Understand(opn) command returns the understood rules list for opn. The opn parameter must be one of Diff, diff, Int, int, Limit, or limit.

The Understand(opn, all) command adds all possible rules that can be added to the understood rules list for opn.

The Understand(opn, none) command clears the understood rules list for opn.

Otherwise, each rule argument is added to the understood rules list for opn.

This routine returns an equation, or expression sequence of equations, whose left-hand side is the name of the operation and whose right-hand side is the current list of understood rules for that operation.

Each rule argument can be the name of any built-in rule for the corresponding operation that does not require a parameter. For example, the product rule can be added to the understood rules list for Diff, but the change rule cannot be added to the understood rules list for Int, because this rule requires a parameter.  The complete lists of rules for each operation are available on Differentiation Rules, Integration Rules, and Limit Rules.

Additionally, the rules flip and join, which are used in definite integration problems, cannot be added to the understood rules list for Int.

You can also specify the name of any univariate function recognized by Maple as a rule argument. For example, you can add sin or exp to the understood rules list for any of the operations.

It is recommended that you use the Maple userinfo system, by setting infolevel[Student] := 1 or infolevel[Student[Calculus1]] := 1. This displays informative messages in the form of userinfo output from Calculus1 routines as you solve complicated problems.

$\mathrm{with}\left(\mathrm{Student}\left[\mathrm{Calculus1}\right]\right)\:$

$\mathrm{infolevel}\left[\mathrm{Student}\left[\mathrm{Calculus1}\right]\right]≔1\:$

$\mathrm{Understand}\left(\mathrm{diff}\,\mathrm{constant}\,\mathrm{`c*`}\,\mathrm{`+`}\right)$

$\mathrm{Diff}=\left[\mathrm{constant}\,\mathrm{constantmultiple}\,\mathrm{sum}\right]$

$\mathrm{Diff}\left(x^2\sin \left(x\right)+3\cos \left(x\right)\,x\right)$

$\frac{\ⅆ}{\ⅆx}\left(x^2\sin \left(x\right)+3\cos \left(x\right)\right)$

$\mathrm{Rule}\left[\right]\left(\right)$

Creating problem #1

$\frac{\ⅆ}{\ⅆx}\left(x^2\sin \left(x\right)+3\cos \left(x\right)\right)=\frac{\ⅆ}{\ⅆx}\left(x^2\sin \left(x\right)\right)+3\frac{\ⅆ}{\ⅆx}\cos \left(x\right)$

$\mathrm{Rule}\left[\mathrm{`*`}\right]\left(\mathrm{Diff}\left(x^3\left(x^2+2\right)\,x\right)\right)$

Creating problem #2

$\frac{\ⅆ}{\ⅆx}\left(x^3\left(x^2+2\right)\right)=\left(\frac{\ⅆ}{\ⅆx}\left(x^3\right)\right)\left(x^2+2\right)+x^3\left(\frac{\ⅆ}{\ⅆx}\left(x^2\right)\right)$

$\mathrm{Understand}\left(\mathrm{Diff}\right)$

Understood rules for Diff: [constant, constantmultiple, sum]
Other rules for Diff: {Int, chain, power, product, difference, identity, quotient}
The name of any univariate function can also be specified

$\mathrm{Diff}=\left[\mathrm{constant}\,\mathrm{constantmultiple}\,\mathrm{sum}\right]$

$\mathrm{Understand}\left(\mathrm{Diff}\,\mathrm{none}\right)$

$\mathrm{Diff}=\left[\right]$

$\mathrm{Understand}\left(\mathrm{Limit}\,\exp \right)$

$\mathrm{Limit}=\left[\exp \right]$

$\mathrm{Rule}\left[\mathrm{`+`}\right]\left(\mathrm{Limit}\left(x^2+\exp \left(\sin \left(x\right)\right)\,x=1\right)\right)$

Creating problem #3

$\underset{x\to 1}{lim}\left(x^2+{\ⅇ}^{\sin \left(x\right)}\right)=\left(\underset{x\to 1}{lim}{x}^2\right)+{\ⅇ}^{\underset{x\to 1}{lim}\sin \left(x\right)}$

$\mathrm{Understand}\left(\mathrm{Diff}\,\mathrm{chain}\right)$

$\mathrm{Diff}=\left[\mathrm{chain}\right]$

$\mathrm{Diff}\left(\sin \left(x^2\right)\,x\right)$

$\frac{\ⅆ}{\ⅆx}\sin \left(x^2\right)$

$\mathrm{Rule}\left[\sin \right]\left(\right)$

Creating problem #4

Rule [sin] does not apply; you may need to use the chain rule first

$\frac{\ⅆ}{\ⅆx}\sin \left(x^2\right)=\frac{\ⅆ}{\ⅆx}\sin \left(x^2\right)$