Part 1/5:

Understanding Derivative Rules: Constant Multiple, Sum, and Difference Rules

In this article, we'll delve into the foundational rules of derivatives in calculus, specifically focusing on the Constant Multiple, Sum, and Difference rules. These rules are essential for anyone looking to simplify the process of finding derivatives of functions, and we will clarify how they work through examples.

Constant Multiple Rule

The Constant Multiple rule states that if you have a function ( f(x) ) expressed in the form ( f(x) = c \cdot g(x) ), where ( c ) is a constant and ( g(x) ) is any differentiable function, then the derivative of ( f(x) ) can be simplified.

Deriving the Rule

To derive this, we begin with the definition of the derivative:

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