(*********************************************************************** Mathematica-Compatible Notebook This notebook can be used on any computer system with Mathematica 3.0, MathReader 3.0, or any compatible application. The data for the notebook starts with the line of stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). 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For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. ***********************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 9237, 322]*) (*NotebookOutlinePosition[ 33608, 1181]*) (* CellTagsIndexPosition[ 33564, 1177]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell[TextData[{ "Derivatives in ", StyleBox["Mathematica", FontSlant->"Italic"] }], "Title"], Cell["By Robin Sue Sanders (Spring 1998)", "Subsubtitle", TextAlignment->Center], Cell[TextData[{ StyleBox["Mathematica", FontSlant->"Italic"], " knows all about taking derivatives of standard functions. It knows the \ basic derivatives. In other words, ", StyleBox["Mathematica", FontSlant->"Italic"], " knows ", Cell[BoxData[ \(TraditionalForm\`d\/dx\ x\^k\)]], ", ", Cell[BoxData[ \(TraditionalForm\`d\/dx\ Sin[x]\)]], ", ", Cell[BoxData[ \(TraditionalForm\`\(d\/dx\) Cos[x]\)]], ", ", Cell[BoxData[ \(TraditionalForm\`d\/dx\)]], " Tan[x], as well as the derivatives of the other three trig functions. ", StyleBox["Mathematica", FontSlant->"Italic"], " also knows the derivatives of the new fucntions we'll study in Chapters \ 7&8 of the Math 162 text: exponential functions, logarithmic functions, and \ inverse trig functions. ", StyleBox["Mathematica", FontSlant->"Italic"], " also knows all the basic derivative rules for finding derivatives, \ including the Product Rule and the Chain Rule. And finally, ", StyleBox["Mathematica", FontSlant->"Italic"], " knows ", StyleBox["when", FontSlant->"Italic"], " to apply each rule! Fortunately for Calculus students, the name (and \ snytax) for the derivative command is pretty simple." }], "Text"], Cell[CellGroupData[{ Cell[TextData[ "Basic syntax for D[ ]\[LongDash]the derivative command"], "Section"], Cell[TextData[{ "If you want to have ", StyleBox["Mathematica", FontSlant->"Italic"], " take derivatives for you, the syntax is:" }], "Text"], Cell[TextData[{ "\t\tD[function, x]\t\t(Linear Input. Note the use of square\n\t\t\t\t\t \ brackets since D[ ] is a ", StyleBox["Mathematica", FontSlant->"Italic"], " \n\t\t\t\t\t function.)\nor\n\t\t", Cell[BoxData[ \(TraditionalForm\`\[PartialD]\_x\ \((function)\)\)]], "\t\t(Standard input using the ", Cell[BoxData[ \(TraditionalForm\`\[PartialD]\_\[Placeholder]\ \[Placeholder]\)]], "\ttemplate.\n\t\t\t\t\t Note the use of round parenthesis if the \n\t\t\t\ \t\t function has more than one term.)" }], "Text"], Cell[TextData[{ "The \"x\" in each of these commands is ", StyleBox["critical", FontSlant->"Italic"], "\[LongDash]it tells ", StyleBox["Mathematica", FontSlant->"Italic"], " what variable you are differentiating with respect to. In other words, \ D[function, x] says to find ", Cell[BoxData[ \(TraditionalForm\`d\/dx\)]], "function. If you want to differentitate with respect to a variable not \ named \"x\", the name of the appropriate variable should replace the \"x\" in \ the syntax. (See the second example.) 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Note the use of the Chain Rule in ", StyleBox["Mathematica", FontSlant->"Italic"], "'s answer." }], "Text"], Cell[BoxData[ \(\[PartialD]\_x\ Cos[x\^2 + \ x\ + \ 3]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["The \"differentiation\" variable.", "Section"], Cell[TextData[{ "All derivatives are taken ", StyleBox["with respect to a particular variable.", FontSlant->"Italic"], " The syntax for the D[ ] command (or the ", Cell[BoxData[ \(TraditionalForm\`\[PartialD]\_\[Placeholder]\ \[Placeholder]\)]], " command) requires that you specify the \"differentiation\" variable." }], "Text"], Cell[TextData[{ "When using the D[ ] function, the second argument is the \"differentiation\ \" variable. 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The \"Hyperlink\" style is for links within the same Notebook, \ or between Notebooks.\ \>", "Text"], Cell[CellGroupData[{ Cell[StyleData["Hyperlink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`NotebookLocate[ #2]}]&), Active->True, ButtonNote->ButtonData}], Cell[StyleData["Hyperlink", "Presentation"]], Cell[StyleData["Hyperlink", "Condensed"]], Cell[StyleData["Hyperlink", "Printout"], FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell["\<\ The following styles are for linking automatically to the on-line \ help system.\ \>", "Text"], Cell[CellGroupData[{ Cell[StyleData["MainBookLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "MainBook", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["MainBookLink", "Presentation"]], Cell[StyleData["MainBookLink", "Condensed"]], Cell[StyleData["MainBookLink", "Printout"], FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["AddOnsLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontFamily->"Courier", FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "AddOns", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["AddOnsLink", "Presentation"]], Cell[StyleData["AddOnsLink", "Condensed"]], Cell[StyleData["AddOnLink", "Printout"], FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["RefGuideLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontFamily->"Courier", FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "RefGuideLink", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["RefGuideLink", "Presentation"]], Cell[StyleData["RefGuideLink", "Condensed"]], Cell[StyleData["RefGuideLink", "Printout"], FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["GettingStartedLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "GettingStarted", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["GettingStartedLink", "Presentation"]], Cell[StyleData["GettingStartedLink", "Condensed"]], Cell[StyleData["GettingStartedLink", "Printout"], FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["OtherInformationLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "OtherInformation", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["OtherInformationLink", "Presentation"]], Cell[StyleData["OtherInformationLink", "Condensed"]], Cell[StyleData["OtherInformationLink", "Printout"], FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell["Placeholder Styles", "Section"], Cell["\<\ The cells below define styles useful for making placeholder \ objects in palette templates.\ \>", "Text"], Cell[CellGroupData[{ Cell[StyleData["Placeholder"], Editable->False, Selectable->False, StyleBoxAutoDelete->True, Placeholder->True, StyleMenuListing->None], Cell[StyleData["Placeholder", "Presentation"]], Cell[StyleData["Placeholder", "Condensed"]], Cell[StyleData["Placeholder", "Printout"]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["SelectionPlaceholder"], Editable->False, Selectable->False, StyleBoxAutoDelete->True, Placeholder->Primary, StyleMenuListing->None, DrawHighlighted->True], Cell[StyleData["SelectionPlaceholder", "Presentation"]], Cell[StyleData["SelectionPlaceholder", "Condensed"]], Cell[StyleData["SelectionPlaceholder", "Printout"]] }, Closed]], Cell["FormatType Styles", "Section"], Cell["\<\ The cells below define styles that are mixed in with the styles \ of most cells. If a cell's FormatType matches the name of one of the styles \ defined below, then that style is applied between the cell's style and its \ own options. This is particularly true of Input and Output.\ \>", "Text"], Cell[StyleData["CellExpression"], PageWidth->Infinity, CellMargins->{{6, Inherited}, {Inherited, Inherited}}, ShowCellLabel->False, ShowSpecialCharacters->False, AllowInlineCells->False, AutoItalicWords->{}, StyleMenuListing->None, FontFamily->"Courier", FontSize->12, Background->GrayLevel[1]], Cell[StyleData["InputForm"], AllowInlineCells->False, StyleMenuListing->None, FontFamily->"Courier"], Cell[StyleData["OutputForm"], PageWidth->Infinity, TextAlignment->Left, LineSpacing->{0.6, 1}, StyleMenuListing->None, FontFamily->"Courier"], Cell[StyleData["StandardForm"], LineSpacing->{1.25, 0}, StyleMenuListing->None, FontFamily->"Courier"], Cell[StyleData["TraditionalForm"], LineSpacing->{1.25, 0}, SingleLetterItalics->True, TraditionalFunctionNotation->True, DelimiterMatching->None, StyleMenuListing->None], Cell["\<\ The style defined below is mixed in to any cell that is in an \ inline cell within another.\ \>", "Text"], Cell[StyleData["InlineCell"], TextAlignment->Left, ScriptLevel->1, StyleMenuListing->None], Cell[StyleData["InlineCellEditing"], StyleMenuListing->None, Background->RGBColor[1, 0.749996, 0.8]] }], MacintoshSystemPageSetup->"\<\ 00<0004/0B`000002mT8o?mooh<" ] (*********************************************************************** Cached data follows. If you edit this Notebook file directly, not using Mathematica, you must remove the line containing CacheID at the top of the file. 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