** suivant:** Integration
** monter:** Derivative and partial derivative
** précédent:** Derivative and first order
** Table des matières**
** Index**

###

Derivative and *n*-th order
partial derivative : `diff derive deriver`

`derive` (or `diff`) may take more than two arguments : an
expression and the names of the derivation variables (each variable
may be followed by $*n* to indicate the number *n* of derivations).

`diff` returns the partial derivative of the expression with respect to
the variables given after the first argument.
The notation $ is usefull if you want to derive *k* times with
respect to the same variable, instead of entering *k* times the
same variable name, one enters the variable name followed by `$k`,
for example `x$3` instead of `(x,x,x)`.
Each variable may be followed by a $, for example
`diff(exp(x*y),x$3,y$2,z)` is the same as
`diff(exp(x*y),x,x,x,y,y,z)`

**Examples**

- Compute :

Input :
`diff(x*y ``^`

2*z`^`

3+x*y*z,x,z)

Output :
`y``^`

2*3*z`^`

2+y

- Compute :

Input :
`diff(x*y ``^`

2*z`^`

3+x*y*z,x,z,z)

Or input :
`diff(x*y ``^`

2*z`^`

3+x*y*z,x,z$2)

Output :
`y``^`

2*3*2*z

- Compute the third derivative of :

Input :
`normal(diff((1)/(x``^`

2+2),x,x,x))

Or :
`normal(diff((1)/(x``^`

2+2),x$3))

Output :
`(-24*x``^`

3+48*x)/(x`^`

8+8*x`^`

6+24*x`^`

4+32*x`^`

2+16)

**Remark**

** suivant:** Integration
** monter:** Derivative and partial derivative
** précédent:** Derivative and first order
** Table des matières**
** Index**
giac documentation written by Renée De Graeve and Bernard Parisse