Calculus: Why the Derivative of a Constant is Always 0

derivative of a constant:d/dx [c] = ___________________

0

The derivative of a constant is always 0. This is because the derivative measures the rate of change of a function at a particular point, and a constant function has no change (or a rate of change of 0). Therefore, the derivative of any constant c with respect to x is equal to 0, since the function’s value is not affected by changes in x.

In mathematical symbols:

d/dx [c] = 0

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