The Derivative Sum Rule | Simplifying the Process of Finding Derivatives

derivative sum rule, h(x)= f(x) + g(x)

The derivative sum rule states that if you have two functions, let’s call them f(x) and g(x), and you want to find the derivative of their sum, which is h(x) = f(x) + g(x), then you can find the derivative of each function separately and add them together

The derivative sum rule states that if you have two functions, let’s call them f(x) and g(x), and you want to find the derivative of their sum, which is h(x) = f(x) + g(x), then you can find the derivative of each function separately and add them together.

Mathematically, this rule can be expressed as:

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

In simpler terms, if you want to find the derivative of h(x), you can find the derivative of f(x) and the derivative of g(x) individually, and then add them together.

For example, let’s say we have h(x) = 2x^3 + 5x^2. In this case, f(x) would be 2x^3 and g(x) would be 5x^2. To find the derivative of h(x), we apply the derivative sum rule:

d/dx [h(x)] = d/dx [2x^3 + 5x^2]
= d/dx [2x^3] + d/dx [5x^2]
= 6x^2 + 10x

So, the derivative of h(x) is 6x^2 + 10x.

This rule is especially useful when you have a function that is the sum of multiple terms, as it allows you to find the derivative of each term separately and then combine them.

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