derivative of a constant
The derivative of a constant is zero
The derivative of a constant is zero. To explain this, let’s recall what a derivative represents.
The derivative of a function measures the rate at which the function’s value changes with respect to its independent variable (usually x). In other words, it tells us how the function is changing as we move along the x-axis.
A constant function, by definition, has a fixed value regardless of the input. For example, the function f(x) = 5 is a constant function, where f(x) is always equal to 5, regardless of the value of x.
Since the value of the constant function does not change as we move along the x-axis, the rate of change of the function is always zero. Hence, the derivative of any constant function is zero.
Mathematically, if c is a constant, then the derivative of f(x) = c with respect to x is:
f'(x) = 0
To summarize, the derivative of a constant is always zero because the function does not change as the independent variable varies.
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