Differentiation by rule

The rate of change of f(x) with respect to x is measured by the derived function, which is denoted by f'(x).

Where y = f(x), notations for the derived function are f'(x), f', y'(x), y', ,

The most common rate of change of one variable with respect to another that you will meet is the gradient of a curve (at a point), defined to be the gradient of the tangent to the curve at that point.

When x = a, the graph of y = f(x) has height f(a) and the gradient of the curve at the point (a, f(a)) is f'(a).