Think of Derivative as a function which inputs a function and outputs a function. When you think "derivative of 5 is 0", you imply "derivative of f(x)=5 is f'(x

Think of Derivative as a function which inputs a function and outputs a function. When you think "derivative of 5 is 0", you imply "derivative of f(x)=5 is f'(x)=0" This article seems to define a function called Derivative which inputs a number and outputs a number. In this case, "derivative of 5 is 1" actually translates to "derivative of 5 is 1".