Differentiation Rules - Maple Help
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Differentiation Rules for Calculus1

 

Rules

Examples

Rules

• 

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.

Rule

Alternate Names

Description

chain

 

constant

 

constantmultiple

``

difference

identity

int

power

product

quotient

sum

  

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, , , ...]

  

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 , where the exponent (at least) depends on the differentiation variable, as an exponential.  The rule would thus be given as:

     [rewrite,  ]

  

Note: The Rule routine does not attempt to validate the rewrite rules you provide.

Examples

Creating problem #1

(1)

(2)

(3)

If the operation type is ambiguous, Maple returns an error

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

(4)

(5)

Creating problem #3

Rule [power] does not apply

(6)

Creating problem #4

(7)

This example illustrates how to handle an unknown univariate function.

Creating problem #5

(8)

(9)

(10)

The current problem is complete

See Also

diff

Diff

Student

Student[Calculus1]

Student[Calculus1][DiffTutor]

Student[Calculus1][SingleStepOverview]

 


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