if f(x)= log(base2)x find f ' (1)

Question

using implicit differentiation

Answer 1

 

Hi Alexys,

 

     f'(1) = lim_Δx→0 [f(1+Δx) - f(1)]/[(1+Δx) - 1]

 

            = lim_Δx→0 [log₂(1+Δx) - log₂(1)]/Δx

 

            = lim_Δx→0 log₂(1+Δx)/Δx

 

            = lim_Δx→0 log₂(1+Δx)^(1/Δx)

 

            = log₂e

 

            = 1/ln2

 

            = 1.4427