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Optimization for Machine Learning with NumPy and SciPy

Differentiation of the Univariate Functions

Explore the concept of differentiation for univariate functions including derivatives of common functions and key rules. Understand numerical approximation using the central difference formula and implement derivative calculations with SciPy to support machine learning optimization tasks.

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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)(x−6)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 x ...