Question

find the derivative of each of the following from the first principal :

1 (ax+b)

Answer 1

Let ax+b=f(x)
derivative of f(x)=a=[a(1)+0=a]

Answer 2

f(x) = ax + b
f(0) = b
f '(x) =  lim    {f(x) - f(0)} / x
          x---->0
f '(x) = lim     (ax + b - b) / x
          x---->0
f '(x)  = lim      a
           x---->0
f '(x)  = a