derivative of a constant
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The derivative of a constant is always zero.
Remember the definition of a derivative is the rate of change of a function with respect to its independent variable. Since a constant has a fixed value and does not change, its rate of change with respect to any variable is zero.
For example, let’s say we have the function f(x) = 5. No matter what value of x we plug in, the value of f(x) will always be 5. Therefore, the rate of change of f(x) with respect to x is always zero, and the derivative of f(x), denoted as f'(x), is also zero:
f'(x) = 0
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