What exactly is Calculus' Constant Rule? Well, if c is a constant, f(x) is a function, then the derivative of the fuction g(x)=c f(x) will be:

 

 

In the above we take the constant out of the g(x), and these two are equivalent.

Let's look into another situation. (Here we are not looking at the same function mentioned above any more.)

If  f(x)= c, which means the function is just a constant, the graph of the function is basically a horizontal line. then the function's derivative equals 0.

d/dx f(x) = 0 if f(x)=c (where c is a constant)

Note: d/dx f(x) is same as f'(x), just another way of writing derivatives...