Differentiate the parametric function and find dy/dx and d 2 y / d x 2 Differentiate the parametric function and find d y d x and d 2 y d x 2 in terms of "t" when: x = 1 t − 1 and y = 1 t + 1 I have first started by finding d y d x by finding d x d t and d y d t which comes to d x d t = ln ⁡ | t − 1 | and d y d t = ln ⁡ | t + 1 | and used d y d x = d y / d t d x / d t , which gives d y d x = ln ⁡ | t + 1 | ln ⁡ | t − 1 | now if I divide them by each other doesn't it equal to 0? What have I done wrong here?

Question

Differentiate the parametric function and find dy/dx and       d    2    y      /    d      x    2  Differentiate the parametric function and find                     d            y                      d            x       and                               d                2            y                      d                    x        2             in terms of &quot;t&quot; when:  x  =      1          t      −      1       and   y  =      1          t      +      1      I have first started by finding                     d            y                      d            x       by finding                     d            x                      d            t       and                     d            y                      d            t       which comes to                    d            x                      d            t        =  ln  ⁡      |    t  −  1      |  and                     d            y                      d            t        =  ln  ⁡      |    t  +  1      |  and used                     d            y                      d            x        =                    d            y              /                    d            t                      d            x              /                    d            t      , which gives                    d            y                      d            x        =            ln      ⁡              |            t      +      1              |                    ln      ⁡              |            t      −      1              |             now if I divide them by each other doesn&#039;t it equal to 0? What have I done wrong here?

humanistex3 · Accepted Answer

Step 1Given       x    =          1              t        −        1              .  So                     d        x                    d        t              =    −          1              (        t        −        1        )             and       y    =          1              t        +        1            So                     d        x                    d        t              =    −          1              (        t        +        1        )            Now             1      y        −          1      x        =    2        ,  ,Now Diff. both side w. r to x      −          1              y        2                            d        y                    d        x              +          1              x        2              =    0    ⇒                  d        y                    d        x              =                  y        2                    x        2            Now Again Diff. w. r to x, We get                              d          2                y                    d                  x          2                      =          d              d        x                    [                        y          2                          x          2                    ]        =                            x          2                ⋅        2        y                              d            y                                d            x                          −                  y          2                ⋅        2        x                    x        4              =                  2                  y          3                −        2        x                  y          2                            x        4            Step 2Above we have put value f                     d        y                    d        x              =                  y        2                    x        2            . So we get                              d          2                y                    d                  x          2                      =                  2                  y          3                −        2        x                  y          2                            x        4

Waylon Ruiz · Accepted Answer

Step 1Given       x    =          1              t        −        1             and       y    =          1              t        +        1             the differentiation of       x    n   is   n      x          n      −      1      here   x  =      1          t      −      1        =  (  t  −  1      )          −      1      Step 2So             d      x              d      t        =            d      (      t      −      1              )                  −          1                            d      t        =            d      (      t      −      1              )                  −          1                            d      (      t      −      1      )        .            d      (      t      −      1      )              d      t         =  (  −  1  )  (  t  −  1      )          −      1      −      1        .  (  1  )   =  −  (  t  −  1      )          −      2         =            −      1              (      t      −      1              )                  2                    Similarly you can do with Y and then for   d      x          2       and   d      y          2

Differentiate the parametric function and find dy/dx and d 2 </msup> y <mrow

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