jagomart
digital resources
picture1_Calculus Pdf 168676 | 03   Implicit Differentiation


 151x       Filetype PDF       File size 0.04 MB       Source: cdn.kutasoftware.com


File: Calculus Pdf 168676 | 03 Implicit Differentiation
kuta software infinite calculus name implicit differentiation date period dy for each problem use implicit differentiation to find in terms of x and y dx 1 2x3 2y2 5 2 ...

icon picture PDF Filetype PDF | Posted on 25 Jan 2023 | 2 years ago
Partial capture of text on file.
                                                                                                                                
                                        
                       Kuta Software - Infinite Calculus                                                                                                                                                                  Name___________________________________
                       Implicit Differentiation                                                                                                                                                                                                                Date________________  Period____
                                                                                                                                                                                                      dy
                       For each problem, use implicit differentiation to find                                                                                                                                   in terms of x and y.
                                                                                                                                                                                                      dx
                       1)  2x3 = 2y2 + 5                                                                                                                                                             2)  3x2 + 3y2 = 2
                       3)  5y2 = 2x3 − 5y                                                                                                                                                            4)  4x2 = 2y3 + 4y
                       5)  5x3 = −3xy + 2                                                                                                                                                            6)  1 = 3x + 2x2y2
                       7)  3x2y2 = 4x2 − 4xy                                                                                                                                                         8)  5x3 + xy2 = 5x3y3
                                          3          (                        )2                                                                                                                                       2          (         2 3                   )2
                       9)  2x  =  3xy + 1                                                                                                                                                            10)  x  =  4x y  + 1
©u E2a0N1D3J XKbuttrau uSRoNfZtYwjakrJe5 dLBLVCR.a y 9Aul8lw YriisgThDtQsB trGe3steYrQvlePd9.i q CMQaBdees qw4igt9hg kIOn1fhiHnGiCtteO zCaaFldcKuclDuOse.M                                    -1-                                                                                                                                                 Worksheet by Kuta Software LLC
                                                                                                                
                                        
                        11)  sin 2x2y3 = 3x3 + 1                                                                                                                                                        12)  3x2 + 3 = ln 5xy2
                                                                                                                                                                                                              22
                                                                                                                                                                                                         d22y
                        For each problem, use implicit differentiation to find                                                                                                                                   22  in terms of x and y.
                                                                                                                                                                                                         dx22
                        13)  4y2 + 2 = 3x2                                                                                                                                                              14)  5 = 4x2 + 5y2
                        Critical thinking question:
                                                                                                                            dy                                                                                            3x2
                        15)  Use three strategies to find                                                                            in terms of x and y, where                                                                         = x.  Strategy 1: Use implicit differentiation
                                                                                                                            dx                                                                                              4y
                                      directly on the given equation.  Strategy 2:  Multiply both sides of the given equation by the denominator of
                                      the left side,  then use implicit differentiation.  Strategy 3: Solve for y, then differentiate.  Do your three
                                      answers look the same?  If not, how can you show that they are all correct answers?
©F z2n0H1J37 xKiuvtgaz 8SDoCfutswJalrYek ZLvLFCk.X h cAXlBlv 7rviEg8hytusU erRessneuruvgeRd0.l J RMIaVd3e9 iw3iXtlhC OIJnafJi9nGictgea wCPa8lbcYuqlJu7sN.i                                       -2-                                                                                                                                                   Worksheet by Kuta Software LLC
                                                                                                                                                                                                                                                                                                                                    
                                        
                       Kuta Software - Infinite Calculus                                                                                                                                                                  Name___________________________________
                       Implicit Differentiation                                                                                                                                                                                                                Date________________  Period____
                                                                                                                                                                                                      dy
                       For each problem, use implicit differentiation to find                                                                                                                                   in terms of x and y.
                                                                                                                                                                                                      dx
                       1)  2x3 = 2y2 + 5                                                                                                                                                             2)  3x2 + 3y2 = 2
                                        dy               3x2                                                                                                                                                         dy                     x
                                                 =                                                                                                                                                                            = −
                                        dx                2y                                                                                                                                                         dx                     y
                       3)  5y2 = 2x3 − 5y                                                                                                                                                            4)  4x2 = 2y3 + 4y
                                        dy                    6x2                                                                                                                                                    dy                       4x
                                                 =                                                                                                                                                                            = 
                                        dx               10y + 5                                                                                                                                                     dx               3y2 + 2
                       5)  5x3 = −3xy + 2                                                                                                                                                            6)  1 = 3x + 2x2y2
                                        dy               −y − 5x2                                                                                                                                                    dy               −3 − 4xy2
                                                 =                                                                                                                                                                            = 
                                        dx                           x                                                                                                                                               dx                       4x2y
                       7)  3x2y2 = 4x2 − 4xy                                                                                                                                                         8)  5x3 + xy2 = 5x3y3
                                        dy               4x − 2y − 3xy2                                                                                                                                              dy               15x2y3 − 15x2 − y2
                                                 =                                                                                                                                                                            = 
                                        dx                       3x2y + 2x                                                                                                                                           dx                         2xy − 15x3y2
                                          3          (                        )2                                                                                                                                       2          (         2 3                   )2
                       9)  2x  =  3xy + 1                                                                                                                                                            10)  x  =  4x y  + 1
                                        dy               −3y2x − y + x2                                                                                                                                              dy               −32y6x2 − 8y3 + 1
                                                 =                                                                                                                                                                            = 
                                        dx                         3x2y + x                                                                                                                                          dx                   48x3y5 + 12xy2
©a Q2V0q1F3G pKHuutPal 6SvorfAt8w3a9rnef kLjLtC4.M d mAQlyl0 9rMiAgJhytvs0 Rr9eZsKePrEvjeedm.M s QMdawd3e7 DwciJtVhU WIbnXfJiQnLivtSe3 1C4a3lbcVuol4uWsr.2                                    -1-                                                                                                                                                 Worksheet by Kuta Software LLC
                                                                                                                                                                                                                                                               
                                        
                       11)  sin 2x2y3 = 3x3 + 1                                                                                                                                                      12)  3x2 + 3 = ln 5xy2
                                        dy               9x − 4y3cos 2x2y3                                                                                                                                           dy               6yx2 − y
                                                 =                                                                                                                                                                            = 
                                        dx                     6xy2cos 2x2y3                                                                                                                                         dx                         2x
                                                                                                                                                                                                           22
                                                                                                                                                                                                      d22y
                       For each problem, use implicit differentiation to find                                                                                                                                 22  in terms of x and y.
                                                                                                                                                                                                      dx22
                       13)  4y2 + 2 = 3x2                                                                                                                                                            14)  5 = 4x2 + 5y2
                                        d2y                  12y2 − 9x2                                                                                                                                              d2y                  −20y2 − 16x2
                                                     =                                                                                                                                                                            = 
                                        dx2                            16y3                                                                                                                                          dx2                                25y3
                       Critical thinking question:
                                                                                                                          dy                                                                                          3x2
                       15)  Use three strategies to find                                                                           in terms of x and y, where                                                                       = x.  Strategy 1: Use implicit differentiation
                                                                                                                          dx                                                                                            4y
                                     directly on the given equation.  Strategy 2:  Multiply both sides of the given equation by the denominator of
                                     the left side,  then use implicit differentiation.  Strategy 3: Solve for y, then differentiate.  Do your three
                                     answers look the same?  If not, how can you show that they are all correct answers?
                                                                           dy               6xy − 4y2                                                              dy               6x − 4y                                                         dy               3
                                       Strategy 1:                                  =                        2              , Strategy 2:                                   =                                , Strategy 3:                                   =              To show all
                                                                           dx                        3x                                                            dx                       4x                                                      dx               4
                                                                                                                                        3x
                                       answers are the same, plug y =                                                                             into results for strategies 1 and 2.
                                                                                                                                          4
                                            Create your own worksheets like this one with                                                                                                                                          .  Free trial available at KutaSoftware.com
                                                                                                                                                                                 Infinite Calculus
©j 9280J163Z IKwubtGax ySRowfMtvwea8rler qLELgCK.M 4 0A2lhlF Mrii2gLhJtBsf vrDepsWeZrMvreodd.l e VMja7dDeG 4wMipt1hY PIDnnfGinnMiEtfeU BCkablzcbumlUuOs8.y                                    -2-                                                                                                                                                 Worksheet by Kuta Software LLC
The words contained in this file might help you see if this file matches what you are looking for:

...Kuta software infinite calculus name implicit differentiation date period dy for each problem use to find in terms of x and y dx xy u eandj xkbuttrau usronfztywjakrje dlblvcr a aullw yriisgthdtqsb trgesteyrqvlepd i q cmqabdees qwigthg kionfhihngictteo zcaafldckuclduose m worksheet by llc sin ln critical thinking question three strategies where strategy directly on the given equation multiply both sides denominator left side then solve differentiate do your answers look same if not how can you show that they are all correct f znhj xkiuvtgaz sdocfutswjalryek zlvlfck h caxlblv rvieghytusu erressneuruvgerd l j rmiavde iwixtlhc oijnafjingictgea wcpalbcyuqljusn...

no reviews yet
Please Login to review.