Differentiation Rules for Calculus1 - Maple Programming Help

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Differentiation Rules for Calculus1

 

Rules

Examples

Rules

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See Student[Calculus1] for a general introduction to the Calculus1 subpackage of the Student package.

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See SingleStepOverview for an introduction to the step-by-step (or single-step) functionality of the Calculus1 package.

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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

 

fgx=fgxgx

constant

 

c=0

constantmultiple

`c*`

cf=cf

difference

`-`

fg=fg

identity

`^`

x=1

int

Int

cxftⅆt' =fx

power

`^`

xn=nxn1

product

`*`

fg=fg+fg

quotient

`/`

fg=gffgg2

sum

`+`

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).

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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, f1x=g1x, f2x=g2x, ...]

  

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

     [rewrite, fxgx=ⅇgxlnfx ]

  

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

Examples

withStudent:-Calculus1:

infolevelStudentCalculus11:

Rule`*`ⅆⅆxx2sinx2

Creating problem #1

ⅆⅆxx2sinx2=ⅆⅆxx2sinx2+x2ⅆⅆxsinx2

(1)

Rulechain

ⅆⅆxx2sinx2=ⅆⅆxx2sinx2+x2ⅆⅆ_X0sin_X0_X0=x2|ⅆⅆ_X0sin_X0_X0=x2ⅆⅆxx2

(2)

Rulesin

ⅆⅆxx2sinx2=ⅆⅆxx2sinx2+x2cosx2ⅆⅆxx2

(3)

If the operation type is ambiguous, Maple returns an error

Rulesumxx2+∫0xcostⅆt

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

Rulesumxx2+∫0xcostⅆt,diff

Creating problem #2

xx2+0xcostⅆt=ⅆⅆxx2+x0xcostⅆt

(4)

Ruleint

xx2+0xcostⅆt=ⅆⅆxx2+cosx

(5)

Rule`^`ⅆⅆxⅇx

Creating problem #3

Rule [power] does not apply

ⅆⅆxexpx=ⅆⅆxexpx

(6)

Rulerewrite,xsinx=ⅇsinxlnxⅆⅆxxsinx

Creating problem #4

ⅆⅆxxsinx=ⅆⅆxⅇsinxlnx

(7)

This example illustrates how to handle an unknown univariate function.

Rule`*`ⅆⅆrrfr

Creating problem #5

ⅆⅆrrfr=ⅆⅆrrfr+rⅆⅆrfr

(8)

Rulef

ⅆⅆrrfr=ⅆⅆrrfr+rⅆⅆrfr

(9)

Ruleidentity

ⅆⅆrrfr=fr+rⅆⅆrfr

(10)

ShowIncomplete

The current problem is complete

See Also

diff

Diff

Student

Student[Calculus1]

Student[Calculus1][DiffTutor]

Student[Calculus1][SingleStepOverview]