Understanding the Difference Rule in Calculus: Derivative of a Difference of Two Functions

Difference Rule

The difference rule is a derivative rule in calculus that helps us find the derivative of a difference of two functions

The difference rule is a derivative rule in calculus that helps us find the derivative of a difference of two functions.

To understand the difference rule, let’s suppose we have two functions f(x) and g(x), and we want to find the derivative of their difference, h(x) = f(x) – g(x).

The difference rule states that the derivative of the difference of two functions is equal to the difference of their derivatives. Mathematically, it can be written as:

h'(x) = f'(x) – g'(x)

In simpler terms, we can find the derivative of h(x) by simply finding the derivatives of f(x) and g(x) separately, and then subtracting one from the other.

To apply the difference rule, we need to know the derivatives of the individual functions f(x) and g(x). The derivative of f(x) is denoted as f'(x) and the derivative of g(x) is denoted as g'(x).

For example, let’s say we have two functions:

f(x) = 3x^2 and g(x) = 4x

We want to find the derivative of their difference, h(x) = f(x) – g(x).

First, we find the derivative of f(x) and g(x) using the power rule and constant multiple rule:

f'(x) = d/dx (3x^2) = 6x
g'(x) = d/dx (4x) = 4

Now, we can apply the difference rule to find the derivative of h(x):

h'(x) = f'(x) – g'(x)
= 6x – 4

So, the derivative of h(x) is h'(x) = 6x – 4.

This means that for any value of x, the slope of the tangent line to the graph of h(x) is equal to 6x – 4.

The difference rule is a straightforward and useful formula that allows us to find the derivative of a difference of two functions without much complexity. It is one of the fundamental rules in calculus and is commonly used in many mathematical and scientific applications.

More Answers: