Utilizing the Constant Multiple Rule to Simplify Math Calculations

Constant Multiple Rule

The constant multiple rule is a mathematical rule that applies to the multiplication of a constant with a function

The constant multiple rule is a mathematical rule that applies to the multiplication of a constant with a function. It states that if you have a constant, let’s say “c”, and a function, let’s say “f(x)”, then the product of the constant and the function is equal to the constant multiplied by the value of the function.

In mathematical notation, the constant multiple rule can be written as: c * f(x) = cf(x)

Here, “c” represents the constant and “f(x)” represents the function. The result is obtained by multiplying the constant with the value of the function at any given point.

For example, let’s consider the function f(x) = 2x. If we apply the constant multiple rule and multiply the function by a constant, say 3, we get:

3 * f(x) = 3 * 2x = 6x

So, the constant multiple rule tells us that multiplying a function by a constant results in the constant being multiplied by every term in the function.

This rule is particularly useful in calculus when dealing with derivatives and integrals. When taking the derivative or integral of a function multiplied by a constant, we can apply the constant multiple rule to simplify the calculations.

For example, if we have the function f(x) = 5x^2, and we want to find the derivative, we can multiply the function by the constant 5 and apply the constant multiple rule as follows:

d/dx (5x^2) = 5 * d/dx (x^2) = 5 * 2x = 10x

In summary, the constant multiple rule states that when multiplying a function by a constant, the result is obtained by multiplying the constant by each term in the function. This rule is particularly useful in simplifying calculations involving derivatives and integrals.

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