Answer:[tex]f'(x)=log_{4}x[/tex]
Step-by-step explanation:
Lets first identify the function using the given data.
Clearly we can see the trend in the data.
The value of the function [tex]f(x)[/tex] is [tex]4^{x}[/tex]
So,[tex]f(x)=4^{x}[/tex]
Now we find the inverse of the function.
Let [tex]f'(x)[/tex] be the inverse function.
Now substitute [tex]f'(x)[/tex] in the place of [tex]x[/tex] and [tex]x[/tex] in the place of [tex]f(x)[/tex] in the above equation.
So,[tex]x=4^{f'(x)}[/tex]
Applying logarithm on both sides,
[tex]ln(x)=f'(x)ln(4)[/tex]
[tex]f'(x)=log_{4}x[/tex]
