Question

f(x) = x^2
g(x) = e^2x
h(x) = ln(2x)
which function is increasing the fastest when x = 2

How do I do this? TIA

I will assume that g(x) = e^2x = e^(2x) and now e^x * x . It is ambiguous the way you have written it

(1) Differentiate each function to get f'(x), g'(x) and h'(x)
(2) Plug in x = 2 to f', g'and h'
(3) See which is biggest

Example:
f'(x) = 2x f'(2) = 4
g'(x) = 2*e^2x g'(2) = 2*e^4 = 109.1

You finish it