# gsw_pt_first_derivatives

`first derivatives of potential temperature`

## USAGE:

`[pt_SA, pt_CT] = gsw_pt_first_derivatives(SA,CT)`

## DESCRIPTION:

```Calculates the following two partial derivatives of potential
temperature (the regular potential temperature whose reference sea
pressure is 0 dbar)
(1) pt_SA, the derivative with respect to Absolute Salinity at
constant Conservative Temperature, and
(2) pt_CT, the derivative with respect to Conservative Temperature at
constant Absolute Salinity.``` ```Click for a more detailed description of the first derivatives of potential temperature.```

## INPUT:

```SA  =   Absolute Salinity                                       [ g/kg ]
CT  =   Conservative Temperature                               [ deg C ]```
`SA & CT need to have the same dimensions.`

## OUTPUT:

```pt_SA =  The derivative of potential temperature with respect to
Absolute Salinity at constant Conservative Temperature.
[ K/(g/kg)]
pt_CT =  The derivative of potential temperature with respect to
Conservative Temperature at constant Absolute Salinity.
pt_CT is dimensionless.                            [ unitless ]```

## EXAMPLE:

```SA = [34.7118; 34.8915; 35.0256; 34.8472; 34.7366; 34.7324;]
CT = [28.8099; 28.4392; 22.7862; 10.2262;  6.8272;  4.3236;]```
`[pt_SA, pt_CT] = gsw_pt_first_derivatives(SA,CT)`
`pt_SA =`
```   0.041863223165431
0.041452303483011
0.034682095247246
0.018711079068408
0.014079958329844
0.010577326129948```
`pt_CT =`
```   0.997192967140242
0.997451686508335
0.998357568277750
0.999996224076267
1.000283719083268
1.000525947028218```

## AUTHOR:

`Trevor McDougall and Paul Barker              [ help@teos-10.org ]`

## VERSION NUMBER:

`3.05 (16th February, 2015)`

## REFERENCES:

```IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of
seawater - 2010: Calculation and use of thermodynamic properties.
Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
UNESCO (English), 196 pp.  Available from the TEOS-10 web site.
See Eqns. (A.12.6), (A.12.3), (P.6) and (P.8) of this TEOS-10 Manual.```
`This software is available from http://www.TEOS-10.org`