Derivative of a Linear Function
its slope
The derivative of a linear function is a constant value.
Let’s say we have a linear function f(x) = mx + b, where m is the slope of the line and b is the y-intercept.
To find the derivative of this function, we use the power rule of differentiation. Since the derivative of any constant is 0, we only need to differentiate the x term (since m is a constant).
So, the derivative of f(x) = mx + b is:
f'(x) = m
This means that the derivative of any linear function is a constant value equal to the slope of the line.
For example, if we have a linear function f(x) = 2x + 5, the derivative of this function is:
f'(x) = 2
This means that the slope of the line is 2, and the rate of change of the function at any point is constant and equal to 2.
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