{"text_format":"3","workbook":"xlsx","n_sheets":3,"sheets":["Sheet1","Sheet2","Sheet3"],"not_rendered":{"charts":4,"images":3,"macros":1,"defined_names":7,"comments":1},"read":"whole","date_system":"1900"}

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[null,"     Visualizing the Product Rule"]
[]
[null,"    This DIGMath program helps you visualize "]
[null,"      the Product Rule for finding the derivative"]
[null,null,"of the product of two functions:  "]
[null,null,"   y = f(x)    and    y = g(x)"]
[null,"        on any interval from x = a  to x = b."]
[]
[]
["Enter the first function in terms of x:   y = f(x) =  ",{"$nulls":4},"sin(3*x)"]
[]
["Enter the second function in terms of x:  y = g(x) = ",{"$nulls":4},"x^3"]
[]
[{"$nulls":8},"Now trace along the various curves:"]
["Now enter the interval for x :  ",{"$nulls":7},"x  = ",{"$f":"D16+K15*Sheet2!B12","v":1.1177644710578842},280]
[null,"   Starting value a =",null,0,{"$nulls":4},"f(x) =",{"$f":"LOOKUP(J15,Sheet2!C3:C504,Sheet2!D3:D504)","v":-0.19839952238850211},null,"slope of  f(x) =",{"$f":"LOOKUP(x0,Sheet2!C3:C504,Sheet2!E3:E504)","v":-2.9367293886784376}]
[null,"    Ending value b =",null,2,{"$nulls":4},"g(x) =",{"$f":"LOOKUP(J15,Sheet2!C$3:C$504,Sheet2!F$3:F$504)","v":1.38162257005585},null,"slope of g(x) =",{"$f":"LOOKUP(x0,Sheet2!C3:C504,Sheet2!G3:G504)","v":3.7348217736185436}]
[{"$nulls":8},"f(x)g(x) =",{"$f":"LOOKUP(x0,Sheet2!C$3:C$504,Sheet2!H$3:H$504)","v":-0.27411325802025543},null,"slope of product f∙g is",{"$f":"LOOKUP(x0,Sheet2!C3:C504,Sheet2!I3:I504)","v":-4.842223534946171}]
[]
[{"$nulls":8},"f'(x)g'(x) =",{"$f":"LOOKUP(x0,Sheet2!C$3:C$504,Sheet2!J$3:J$504)","v":-10.968160864061703},null,"f'(x)g(x) + f(x)g'(x) =",{"$f":"LOOKUP(x0,Sheet2!C$3:C$504,Sheet2!K$3:K$504)","v":-4.798438461636545}]
[]
[]
["Click each item below for suggestions and investigations"]
[null,null,"   Item 1"]
[null,null,"   Item 2"]
[null,null,"   Item 3"]
[null,null,"   Item 4"]
[]
[]
[]
["To access/download all the DIGMath Apps for Calculus"]
["     Click this link:",null,"DIGMath for Calculus"]
[]
["Created by:  Sheldon P. Gordon   "]
["                      Farmingdale State College    "]
["Development of this module was supported by the "]
["NSF's Division of Undergraduate Education  "]
["under grants DUE-0310123 and DUE-0442160."]

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