Differentiation Rules for Calculus1
See Student[Calculus1] for a general introduction to the Calculus1 subpackage of the Student package.
See SingleStepOverview for an introduction to the step-by-step (or single-step) functionality of the Calculus1 package.
The following table lists the built-in rules for differentiation that do not take parameters. These rules can be passed as the index to Rule or as a rule argument to Understand.
⁡f⁡g⁡x⁢' =f⁢' ⁢⁡g⁡x⁢g⁢ '⁢⁡x
⁡f−g⁢' =' ⁢f−' ⁢g
⁡f⁢g⁢' =' ⁢f⁢g+' ⁢f⁢g
⁡fg⁢' =⁡' ⁢f⁢g−' ⁢f⁢gg2
⁡f+g⁢' =' ⁢f+' ⁢g
The name of any univariate function can also be used as a rule argument to the Rule command. The name of any univariate function recognized by Maple, for example, sin, can be passed as a rule argument to the Understand command (where recognized means that it is of type mathfunc).
There is one differentiation rule which requires a parameter: rewrite. This rule can be used as the index to a call to Rule, but cannot be given as a rule argument to Understand. This rule is used to change the form of the expression being differentiated. It has the general form:
[rewrite, f1⁡x=g1⁡x, f2⁡x=g2⁡x, ...]
The effect of applying the rewrite rule is to perform each substitution listed as a parameter to the rule, where occurrences of the left-hand side of each substitution are replaced by the corresponding right-hand side.
The main application of this rule is to rewrite an expression of the form f⁡xg⁡x, where the exponent (at least) depends on the differentiation variable, as an exponential. The rule would thus be given as:
[rewrite, f⁡xg⁡x=ⅇg⁡x⁢ln⁡f⁡x ]
Note: The Rule routine does not attempt to validate the rewrite rules you provide.
infolevelStudent[Calculus1] ≔ 1:
Creating problem #1
Error, (in Student:-Calculus1:-Rule[sum]) unable to determine which calculus operation is being applied in this problem; you can provide this information as the 2nd argument on your call to Rule or Hint
Creating problem #2
Creating problem #3
Rule [power] does not apply
Creating problem #4
This example illustrates how to handle an unknown univariate function.
Creating problem #5
The current problem is complete
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