Differential calculus, tangent line. This diagram demonstrates how the tangent to a graphed curve relates to the key mathematical concept of differential calculus. This area of mathematics involves applying a process called differentiation to a mathematical function to determine the rate of change of the function. Here, the mathematical function is the red line f(x), and the tangent is the blue line. The slope of the tangent is the differential f'(x), the rate of change of the function at that point. There are numerous applications of this concept, which was developed as a practical method by Newton and Leibniz in the 17th century.