What is the derivative of a constant c with respect to x?

The derivative of a constant ( c ) with respect to ( x ) is zero. This is because the derivative measures the rate of change of a function with respect to the variable in question. A constant does not change as ( x ) changes; it remains the same value regardless of the value of ( x ). Therefore, there is no change in the value of the function, and the rate of change, which is represented by the derivative, is zero.

In other words, mathematically, the derivative ( \frac{d}{dx}(c) = 0 ), illustrating that the slope of the function at any point is flat, confirming that constants have no contribution to changes in ( x ).