A derivative is the rate of change of a quantity y with respect to another quantity x. A derivative is also termed the differential coefficient of y with respect to x. Differentiation is the process of finding the derivative of a function.
What Are Derivatives?If f(x) is a function differentiable in an interval [a,b], at every point of the interval the derivative of the function exists finitely and it is unique. There exists a new function g: [a,b] → R, such that, x ∈ [a,b], g(x) = f'(x). This f'(x) is the first derivative of the function f(x), that is denoted by df(x)dxdf(x)dx or Df(x) or f'(x).