How do I find the derivative of f ( x ) = 6 x 2 − 1 using the definition of a derivative?

Question

How do I find the derivative of   f  (  x  )  =  6      x    2    −  1 using the definition of a derivative?

kistkalfljw · Accepted Answer

In terms of a derivative      f    ′          (      x      )        =          lim              h        →        0                                      f                      (            x            +            h            )                          -                  f                      (            x            )                              h      We want differentiate                               f                      (            x            )                          =        6                  x          2                -        1            , then      f    ′          (      x      )        =          lim              h        →        0                            6                              (            x            +            h            )                    2                -        1        -                  (          6                      x            2                    -          1          )                    h                          f        ′                  (          x          )                      =          lim              h        →        0                            6                  (                      x            2                    +                      h            2                    +          2          x          h          )                -        1        -        6                  x          2                +        1            h                          f        ′                  (          x          )                      =          lim              h        →        0                            6                  x          2                +        6                  h          2                +        12        x        h        -        1        -        6                  x          2                +        1            h                          f        ′                  (          x          )                      =          lim              h        →        0                            6                  h          2                +        12        x        h            h                          f        ′                  (          x          )                      =          lim              h        →        0                            6                  h          2                    h        +          lim              h        →        0                            12        x        h            h                          f        ′                  (          x          )                      =          lim              h        →        0              6    h    +          lim              h        →        0              12    x                      f        ′                  (          x          )                      =    12    x

How do I find the derivative of f(x)=6x^2-1 using the definition of a derivative?

Answered question

Answer & Explanation

New Questions in Calculus 1