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picture1_Calculus Pdf 169642 | 03   Chain Rule With Trig


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File: Calculus Pdf 169642 | 03 Chain Rule With Trig
kuta software infinite calculus name differentiation trigonometric functions date period differentiate each function with respect to x 3 3 1 f x sin 2x 2 y tan 5x 3 y ...

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                       Kuta Software - Infinite Calculus                                                                                                                                                                  Name___________________________________
                       Differentiation - Trigonometric Functions                                                                                                                                                                                               Date________________  Period____
                       Differentiate each function with respect to x.
                                       ( )                                3                                                                                                                                                                   3
                       1)   f x  = sin 2x                                                                                                                                                            2)  y = tan 5x     
                       3)  y = sec 4x5                                                                                                                                                               4)  y = csc 5x5   
                                              (         5              )                  2                                                                                                                                             2
                       5)  y =  2x  + 3 cos x                                                                                                                                                                               −2x  − 5
                                                                                                                                                                                                     6)  y =                                      3             
                                                                                                                                                                                                                              cos 2x
                                       ( )                       3        5                                                                                                                                                                                    2                 2
                       7)   f x  = sin                                x                                                                                                                                             ( )                          (                            )
                                                                                                                                                                                                     8)   f x  = cos −3x  + 2   
©g p230Y183g UK8uStVa1 qSHo9fotSwyadrZeO GL2LICZ.G 3 3AClulO 2rliHgihitls5 4rde4sYeVrTvmeodM.L d ZMLaedme4 LwBibtqh4 HIhnXfNiPn1iNtuek nCuaSlVcuunleuisQ.P                                                                                                                                                                                        Worksheet by Kuta Software LLC
                                                                                                                                                                                                                                                                                                                                      
    
                        Kuta Software - Infinite Calculus                                                                                                                                                                   Name___________________________________
                        Differentiation - Trigonometric Functions                                                                                                                                                                                                Date________________  Period____
                        Differentiate each function with respect to x.
                                       ( )                                 3                                                                                                                                                                    3
                        1)   f x  = sin 2x                                                                                                                                                            2)  y = tan 5x     
                                             '( )                                   3                2
                                         f        x  = cos 2x  ⋅ 6x                                                                                                                                                    dy                        2            3                    2
                                                 = 6x2cos 2x3                                                                                                                                                                   = sec 5x  ⋅ 15x
                                                                                                                                                                                                                       dx
                                                                                                                                                                                                                            = 15x2 ⋅ sec2 5x3
                        3)  y = sec 4x5                                                                                                                                                               4)  y = csc 5x5   
                                        dy = sec 4x5 ⋅ tan 4x5 ⋅ 20x4                                                                                                                                                  dy = −csc 5x5 ⋅ cot 5x5 ⋅ 25x4
                                        dx                                                                                                                                                                             dx
                                             = 20x4sec 4x5 ⋅ tan 4x5                                                                                                                                                        = −25x4csc 5x5 ⋅ cot 5x5
                                              (          5              )                 2                                                                                                                                               2
                        5)  y =  2x  + 3 cos x                                                                                                                                                                               −2x  − 5
                                                                                                                                                                                                      6)  y =                                       3             
                                        dy                                                                                                                                                                                     cos 2x
                                                        (          5              )                              2                                        2                    4
                                                 =  2x  + 3  ⋅ −1sin x  ⋅ 2x + cos x  ⋅ 10x                                                                                                                                                                 3                            (             2              )                                  3                2
                                        dx                                                                                                                                                                             dy               cos 2x  ⋅ −4x −  −2x  − 5  ⋅ −1sin 2x  ⋅ 6x
                                                                 (             5                  2                             2                  3                  2)                                                        =                                                                                    3
                                             = 2x −2x sin x  − 3sin x  + 5x cos x                                                                                                                                      dx                                                                    cos2 2x
                                                                                                                                                                                                                                                (                              3                  3                     3                                         3)
                                                                                                                                                                                                                                        2x −2cos 2x  − 6x sin 2x  − 15xsin 2x
                                                                                                                                                                                                                            = 
                                                                                                                                                                                                                                                                                           cos2 2x3
                                       ( )                       3        5                                                                                                                                                                                      2                 2
                        7)   f x  = sin                                x                                                                                                                                              ( )                          (                            )
                                                                                                                                                                                                      8)   f x  = cos −3x  + 2   
                                             '( )                                  2        5                  5                4                                                                                                                                           2                 2                          2
                                         f        x  = 3 ⋅ sin                          x cos x  ⋅ 5x                                                                                                                      '( )                               (                            )               (                            )
                                                                                                                                                                                                                       f         x  = −sin −3x  + 2  ⋅ 2 −3x  + 2  ⋅ −6x
                                                 = 15x4 ⋅ sin2 x5cos x5                                                                                                                                                                                               (              2              )2         (              2              )
                                                                                                                                                                                                                                = 12xsin −3x  + 2  ⋅  −3x  + 2
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                                                                                                                                                                                  Infinite Calculus
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