To find the derivative of the function
f(x) = 1x, we first rewrite it as
f(x) = x.
The derivative of a function gives us the rate at which the function is changing at any given point. For the function
f(x) = x, the derivative can be computed using the power rule of differentiation, which states that the derivative of
x^n is
n*x^(n-1).
Here, we can consider our function as
f(x) = x^1. Applying the power rule:
f'(x) = 1 * x^(1-1) = 1 * x^0 = 1.
So, the derivative of
1 x (or just x) is simply
1.
This means that for every unit increase in x, the value of the function f(x) = x increases by 1. It is a linear function with a constant rate of change.