The Difference Rule | How to Find the Derivative of a Function by Subtracting Two Functions

Difference Rule

The difference rule is a fundamental rule in calculus that allows us to find the derivative of a function that is formed by subtracting two other functions

The difference rule is a fundamental rule in calculus that allows us to find the derivative of a function that is formed by subtracting two other functions.

The rule states that if we have two functions, f(x) and g(x), and we want to find the derivative of their difference, which is represented as h(x) = f(x) – g(x), then the derivative of h(x) can be found by taking the derivative of f(x) and subtracting the derivative of g(x) from it.

In mathematical notation, if f'(x) represents the derivative of f(x) and g'(x) represents the derivative of g(x), then the difference rule can be written as:

(h(x))’ = (f(x) – g(x))’ = f'(x) – g'(x)

This rule is based on the fact that the derivative of a constant is zero, so when we subtract the derivative of g(x) from the derivative of f(x), the constant terms cancel out.

The difference rule is a useful tool in calculus as it allows us to calculate the derivatives of functions involving subtraction without having to go through the limit definition of the derivative. It helps to simplify calculations and find rates of change more efficiently.

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