## Derivative

The derivative of a function at a chosen input value describes the best linear approximation of the function near that input value. For a real-valued function of a single real variable, the derivative at a point equals the slope of the tangent line to the graph of the function at that point.

The graph of a function, drawn in black, and a tangent line to that function, drawn in red. The slope of the tangent line is equal to the derivative of the function at the marked point.

The process of finding a derivative is called differentiation. The Fundamental Theorem of Calculus
states that differentiation is the reverse process to integration.

Differentiation is a method to compute the rate at which a quantity,

Differentiation

Differentiation is a method to compute the rate at which a quantity,

*y*, changes with respect to the change in another quantity,*x*, upon which it is dependent. This rate of change is called the derivative of*y*with respect to*x*. In more precise language, the dependency of*y*on*x*means that*y*is a function of*x*. If*x*and*y*are real numbers, and if the graph of*y*is plotted against*x*, the derivative measures the slope of this graph at each point. This functional relationship is often denoted*y*=*f*(*x*), where*f*denotes the function.