Simplifying the second derivativeI need to simplify the below with respect to y ″ . I'm given: y ″ = − 3 x 2 y 3 − 3 x 3 y 2 ( − x 3 y 3 ) y 6 The final result should look like: − 3 x 2 ( y 4 + x 4 ) y 7 Here are my steps:1.Combine term: − 3 x 3 y 2 ( − x 3 y 3 ) − 3 x 3 y 2 ( − x 3 y 3 ) = 3 x 6 y 2 y 3 Our expression is now: y ″ = − 3 x 2 y 3 + 3 x 6 y 2 y 3 y 6 2.Multiply the final term in the numerator, 3 x 6 y 2 y 3 , by the it's reciprocal in the denominator, y 6 1 , to eliminate the complex fraction. 3 x 6 y 2 y 3 ∗ y 6 1 = 3 x 6 y 8 y 3 Our expression is now: y ″ = − 3 x 2 y 3 y 6 + 3 x 6 y 8 y 3 3.Multiply term 3 x 6 y 8 y 3 by y 3 y 3 to make common denominators. 3 x 6 y 8 y 3 ∗ y 3 y 3 = 3 x 6 y 11 y 6 Our separate terms can now be added, and our expression will look like: y ″ = − 3 x 2 y 3 + 3 x 6 y 11 y 6 4.Now factor the numerator, our expression will become: y ″ = − 3 x 2 y 3 ( 1 + x 4 y 8 ) y 6 Have I made a mistake? I'm not sure where to go from here. I need to achieve this expression as stated at the top my question: y ″ = − 3 x 2 ( y 4 + x 4 ) y 7

Question

Simplifying the second derivativeI need to simplify the below with respect to       y    ″  . I&#039;m given:      y    ″    =  −            3              x        2                    y        3            −      3              x        3                    y        2                    (        −                              x            3                                y            3                          )                    y      6      The final result should look like:  −            3              x        2            (              y        4            +              x        4            )              y      7      Here are my steps:1.Combine term:   −  3      x    3        y    2        (    −                  x        3                    y        3              )    −  3      x    3        y    2        (    −                  x        3                    y        3              )    =            3              x        6                    y        2                    y      3      Our expression is now:      y    ″    =  −            3              x        2                    y        3            +                        3                      x            6                                y            2                                    y          3                            y      6      2.Multiply the final term in the numerator,             3              x        6                    y        2                    y      3      , by the it&#039;s reciprocal in the denominator,             y      6        1  , to eliminate the complex fraction.            3              x        6                    y        2                    y      3        ∗            y      6        1    =            3              x        6                    y        8                    y      3      Our expression is now:      y    ″    =  −            3              x        2                    y        3                    y      6        +            3              x        6                    y        8                    y      3      3.Multiply term             3              x        6                    y        8                    y      3       by             y      3              y      3       to make common denominators.            3              x        6                    y        8                    y      3        ∗            y      3              y      3        =            3              x        6                    y                  11                            y      6      Our separate terms can now be added, and our expression will look like:      y    ″    =  −            3              x        2                    y        3            +      3              x        6                    y                  11                            y      6      4.Now factor the numerator, our expression will become:      y    ″    =  −            3              x        2                    y        3            (      1      +              x        4                    y                  8                    )              y      6      Have I made a mistake? I&#039;m not sure where to go from here. I need to achieve this expression as stated at the top my question:      y    ″    =  −            3              x        2            (              y        4            +              x        4            )              y      7

Kitamiliseakekw · Accepted Answer

y    ″    =  −            3              x        2                    y        3            −      3              x        3                    y        2                    (        −                              x            3                                y            3                          )                    y      6        =  −            3              x        2                    y        3            +      3              x        3                    (                              x            3                    y                )                    y      6        =      y    ″    =  −            (                        3                      x            2                                y            4                    +          3                      x            6                          y            )              y      6        =  −            3              x        2                    y        4            +      3              x        6                    y      7        =  −            3              x        2            (              y        4            +              x        4            )              y      7

Simplifying the second derivative I need to simplify the below with respect to y′′. I'm given:y''=-(3x^2y^3-3x^3y^2(-(x^3)/(y^3)))/(y^6} The final result should look like: -(3x^2(y^4+x^4))/(y^7)

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