Find the derivative of x at x = 1.

To find the derivative of the function \( f(x) = x \) at the point \( x = 1 \), we first need to understand what the derivative represents. The derivative measures how a function changes as its input changes, essentially giving us the slope of the function at a specific point.

Calculating the Derivative

The derivative of \( f(x) = x \) is calculated using basic differentiation rules. For the function \( f(x) = x \), the derivative is:

• f'(x) = 1

Evaluating at x = 1

Now, we evaluate the derivative at \( x = 1 \):

• f'(1) = 1

This means that at the point \( x = 1 \), the slope of the function \( f(x) = x \) is 1. In simpler terms, for every unit increase in \( x \), \( f(x) \) increases by 1 unit.

Summary

The derivative of \( x \) at \( x = 1 \) is simply 1, indicating a constant rate of change for this linear function.