1 | initial version |

There is no need to define such a function.

No need for `var('n i')`

either, by the way.

Once you have defined the function `g`

by

```
sage: g(x) = sin(x) + tan(x)
```

you can check that `g`

is a function, and `g(x)`

is the corresponding expression:

```
sage: g
x |--> sin(x) + tan(x)
sage: g(x)
sin(x) + tan(x)
```

and then you can differentiate the function or the expression three times.

The only thing is that the variable with respect to which to differentiate must be specified.

```
sage: g.diff(x, 3)
x |--> 4*(tan(x)^2 + 1)*tan(x)^2 + 2*(tan(x)^2 + 1)^2 - cos(x)
sage: g(x).diff(x, 3)
4*(tan(x)^2 + 1)*tan(x)^2 + 2*(tan(x)^2 + 1)^2 - cos(x)
```

2 | No.2 Revision |

There is no need to define such a function.

No need for `var('n i')`

either, by the way.

Once you have defined the function `g`

by

```
sage: g(x) = sin(x) + tan(x)
```

you can check that `g`

is a function, and `g(x)`

is the corresponding expression:

```
sage: g
x |--> sin(x) + tan(x)
sage: g(x)
sin(x) + tan(x)
```

and then you can differentiate the function or the expression three times.

The only thing is that the variable with respect to which to differentiate must be specified.

```
sage: g.diff(x, 3)
x |--> 4*(tan(x)^2 + 1)*tan(x)^2 + 2*(tan(x)^2 + 1)^2 - cos(x)
sage: g(x).diff(x, 3)
4*(tan(x)^2 + 1)*tan(x)^2 + 2*(tan(x)^2 + 1)^2 - cos(x)
```

If however you want to understand the error you were getting, here is a hint.

When you do `g = g.diff()`

inside a function, it wants to use a local variable `g`

inside the function.

If you want to use a globally defined variable, specify it with `global g`

as follows:

```
sage: def maderive(n):
....: global g
....: for i in range(n):
....: g=g.diff()
....: return g
....:
sage: maderive(3)
x |--> 4*(tan(x)^2 + 1)*tan(x)^2 + 2*(tan(x)^2 + 1)^2 - cos(x)
```

Note that this modifies the function `g`

. After running the above, you get:

```
sage: g
x |--> 4*(tan(x)^2 + 1)*tan(x)^2 + 2*(tan(x)^2 + 1)^2 - cos(x)
```

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