Mastering the Sum and Difference Rule of Derivatives: A Simple Guide for Math Enthusiasts

d/dx [f(x) ± g(x)]

To find the derivative of the sum or difference of two functions, we can apply the sum/difference rule of derivatives

To find the derivative of the sum or difference of two functions, we can apply the sum/difference rule of derivatives.

The sum/difference rule states that the derivative of the sum or difference of two functions is equal to the sum or difference of their derivatives.

Let’s consider the derivative of the sum of two functions, f(x) and g(x):

d/dx [f(x) + g(x)]

Using the sum rule, we can find the derivative of f(x) and g(x) separately, and then add them:

d/dx [f(x)] + d/dx [g(x)]

This can be written as:

f'(x) + g'(x)

So, the derivative of the sum of f(x) and g(x) is equal to the sum of their derivatives.

Now, let’s consider the derivative of the difference of two functions, f(x) and g(x):

d/dx [f(x) – g(x)]

Using the difference rule, we can find the derivative of f(x) and g(x) separately, and then subtract them:

d/dx [f(x)] – d/dx [g(x)]

This can be written as:

f'(x) – g'(x)

So, the derivative of the difference of f(x) and g(x) is equal to the difference of their derivatives.

In summary:

d/dx [f(x) ± g(x)] = f'(x) ± g'(x)

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