Derivative of a constant function

To understand the meaning of a derivative is not easy, but to know how to take derivatives is not difficult. The best way of learning it is, obviously, through practice.

The following table contains a few functions $$f(x)$$ in the first column and its derivatives $$f '(x)$$ in the second one. Look at it and try to complete it:

Solution:$$$ \begin{array} {ll} f(x)=N & f'(x)=0 \\ f(x)=3B & f'(x)=0\end{array}$$$

Note that in all the cases the derivative is zero. The derivative of a constant function is zero, irrespective of the constant. In the last examples, you have seen that $$f (x) =A$$, $$f (x) =N$$ and $$f (x) =3B$$. In all of them the parameter that is changing, $$x$$, does not appear, thus the derivative will always be zero.