Why is the Derivative of a Constant Zero? Explained and Illustrated

d/dx [c]=

The expression d/dx [c] represents the derivative of a constant value “c” with respect to the variable “x

The expression d/dx [c] represents the derivative of a constant value “c” with respect to the variable “x.” When taking the derivative of a constant, the result is always 0.

To understand why the derivative of a constant is 0, let’s recall the definition of derivative. The derivative of a function f(x) with respect to x, denoted as f'(x) or dy/dx, is a measure of how the function changes as the independent variable x changes.

When we have a constant, let’s call it “c,” it means that the value of “c” remains the same regardless of the value of “x.” In other words, the function f(x) = c does not depend on x and is a horizontal line on the graph.

Since the value of c does not change with respect to x, the slope of the line (which represents the rate of change) is always zero. Therefore, the derivative of a constant is 0.

Hence, d/dx [c] = 0.

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