Understanding Derivatives of Linear Functions | Calculating Slope with Differentiation

Derivative of a Linear Function

The derivative of a linear function can be found using the basic rules of differentiation

The derivative of a linear function can be found using the basic rules of differentiation. A linear function has the general form y = mx + b, where m is the slope of the line and b is the y-intercept.

To find the derivative of this linear function, we need to differentiate the equation with respect to x.

The derivative of y = mx + b can be computed as:

dy/dx = d/dx (mx + b)

Since the derivative represents the rate of change of the function, the derivative of a linear function is simply the slope of the line. In this case, the derivative is equal to the coefficient of x, which is m. Therefore, the derivative of a linear function is always a constant value representing the slope of the line.

For example, let’s consider the linear function y = 2x + 3. The derivative of this function is:

dy/dx = d/dx (2x + 3) = 2

This means that the slope of the line represented by this linear function is 2. The derivative tells us that for every 1 unit increase in x, the function increases by 2 units.

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