### Why use symbolic functions?

So, I can do the following by introducing x as a symbolic function.

```
sage: var('b,c,t')
(b, c, t)
sage: x(t) = sqrt(b^2 + c^2*t^2) - b
sage: x
t |--> -b + sqrt(c^2*t^2 + b^2)
sage: diff(x,t)
t |--> c^2*t/sqrt(c^2*t^2 + b^2)
```

I can introduce x as a variable with assigned symbolic values, and get the same result.

```
sage: var('b,c,t')
(b, c, t)
sage: x = sqrt(b^2 + c^2*t^2) - b
sage: x
-b + sqrt(c^2*t^2 + b^2)
sage: diff(x,t)
c^2*t/sqrt(c^2*t^2 + b^2)
```

So, since I can do the same thing using variables, why use symbolic functions at all? Can symbolic functions do things that variables can't do?

Thanks in advance.