The reverse process is called antidifferentiation.

The process of finding a derivative is called differentiation. For a real-valued function of several variables, the Jacobian matrix reduces to the gradient vector. It can be calculated in terms of the partial derivatives with respect to the independent variables. The Jacobian matrix is the matrix that represents this linear transformation with respect to the basis given by the choice of independent and dependent variables. In this generalization, the derivative is reinterpreted as a linear transformation whose graph is (after an appropriate translation) the best linear approximation to the graph of the original function. For this reason, the derivative is often described as the 'instantaneous rate of change', the ratio of the instantaneous change in the dependent variable to that of the independent variable.ĭerivatives can be generalized to functions of several real variables. The tangent line is the best linear approximation of the function near that input value. The derivative of a function of a single variable at a chosen input value, when it exists, is the slope of the tangent line to the graph of the function at that point. For example, the derivative of the position of a moving object with respect to time is the object's velocity: this measures how quickly the position of the object changes when time advances.

Derivatives are a fundamental tool of calculus. In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value).

Graphs plot wolfram mathematica