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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:
| $f (x)$ | $f'(x)$ |
| $1$ | $0$ |
| $5$ | $0$ |
| $230$ | $0$ |
| $0,76$ | $0$ |
| $A$ | $0$ |
| $N$ | ? |
| $3B$ | ? |
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.