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:

$f (x)$	$f^{'} (x)$
$1$	$0$
$5$	$0$
$230$	$0$
$0, 76$	$0$
$A$	$0$
$N$	?
$3 B$	?

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

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 $f (x) = 3 B$ . In all of them the parameter that is changing, $x$ , does not appear, thus the derivative will always be zero.