Find the derivative d d x [ arctan ⁡ ( x 2 + 1 ) ] ( a r c s e c ( x 2 + 1 ) ) 2 1 2 + x 2 1 1 + ( x 2 + ) 2 2 x 1 + ( x 2 + 1 ) 2

Question

Find the derivative       d          d      x        [  arctan  ⁡  (      x    2    +  1  )  ]  (  a  r  c  s  e  c  (      x    2    +  1  )      )    2          1          2      +              x        2                    1          1      +      (              x        2            +              )        2                          2      x              1      +      (              x        2            +      1              )        2

Anaya Gregory · Accepted Answer

Find the derivative of   [  arctan  ⁡  (      x    2    +  1  )  ]  f  (  x  )  =  arctan  ⁡  (  1  +      x    2    )  ⇒      tan          −      1        ⁡  (  1  +      x    2    )    f  (  x  )  =      tan          −      1        ⁡  (  1  +      x    2    )  [  diffrenciate both side  ]        d          d      x        (  f  (  x  )  )  =      d          d      x        (      tan          −      1        ⁡  (  1  +      x    2    )  )      {                                        d                          d              x                                (                      tan                          −              1                                ⁡          (          x          )          )          ⇒                      1                          1              +                              x                2                                                                                      d                          d              x                                (                      x            n                    )          ⇒          n                      x                          (              n              −              1              )                                            }          f    ′    (  x  )  =      1          [      1      +      (      1      +              x        2                    )        2            ]            d          d      x        (  1  +      x    2    )  {      d          d      x        (  c  o  n  s  t  a  n  t  )  =  0  }        f    ′    (  x  )  ⇒            1      (      0      +      2      x      )              1      +      (      1      +              x        2                    )        2              ⇒            2      x              1      +      (      1      +              x        2                    )        2                H  e  n  c  e  ,              d              d        x              [    arctan    ⁡    (    1    +          x      2        )    ]    ⇒                  2        x                    1        +        (                  x          2                +        1                  )          2

Find the derivative (d)/(dx)[arctan(x^2+1)]

Answered question

Answer & Explanation

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