What Is the Derivative of X?

By Staff WriterLast Updated Mar 27, 2020 1:09:22 AM ET

The derivative of x is 1. A derivative of a function in terms of x can be thought of as the rate of change of the function at a value of x. In the case of f(x) = x, the rate of change is 1 at all values of x.

The derivative of a function f(x) is defined as the limit as h tends towards zero of the expression (f(x+h) - f(x))/h.

If f(x) = x, then (f(x+h) - f(x))/h = ((x+h) - x)/h = h/h. For every value of h not equal to zero, h/h is equal to one. Therefore, as h approaches zero, (f(x+h) - f(x))/h = 1.