Differentiation of the Univariate Functions

Learn to calculate derivatives of the univariate functions using finite differences.

Derivatives

A univariate function in mathematics is a function that takes an input variable and produces an output variable. Let’s suppose the position of a car is given by a univariate function f(x)=(x+2)(x6)f(x) = (x+2)(x-6), where xx is time in seconds. In order to calculate the velocity v(x)v(x) of the car at any time xx, we need to compute the instantaneous rate of change of position f(x)f(x) with respect to time xx. For this, we need derivatives.

Given a univariate function f(x)f(x), the derivative df(x)dx\frac{df(x)}{dx} represents the instantaneous rate of change (or instantaneous slope) of the function ff with respect to xx. Mathematically, the derivative of a function ff at a point xx is calculated as follows:

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