Numerical Differentiation

Numerical differentiation is a method used to estimate how a function changes at a specific point by using its nearby values. Instead of calculating the derivative analytically with a formula, it approximates it by looking at small differences between function values at nearby points. Think of it like assessing the speed of a car by checking its position at regular intervals—by seeing how much the position changes over a short time, you estimate the speed. This technique is useful when the exact mathematical expression of the function is unknown or difficult to differentiate analytically.