# gsw_CT_first_derivatives

`first derivatives of Conservative Temperature`

## USAGE:

`[CT_SA, CT_pt] = gsw_CT_first_derivatives(SA,pt)`

## DESCRIPTION:

```Calculates the following two derivatives of Conservative Temperature
(1) CT_SA, the derivative with respect to Absolute Salinity at
constant potential temperature (with pr = 0 dbar), and
(2) CT_pt, the derivative with respect to potential temperature
(the regular potential temperature which is referenced to 0 dbar)
at constant Absolute Salinity.```
 ```Click for a more detailed description of the first derivatives of Conservative Temperature.```

## INPUT:

```SA  =  Absolute Salinity                                        [ g/kg ]
pt  =  potential temperature (ITS-90)                          [ deg C ]
(whose reference pressure is 0 dbar)```
`SA & pt need to have the same dimensions.`

## OUTPUT:

```CT_SA  =  The derivative of Conservative Temperature with respect to
Absolute Salinity at constant potential temperature
(the regular potential temperature which has reference
sea pressure of 0 dbar).
The CT_SA output has units of:                    [ K/(g/kg) ]
CT_pt  =  The derivative of Conservative Temperature with respect to
potential temperature (the regular one with pr = 0 dbar)
at constant SA. CT_pt is dimensionless.           [ unitless ]```

## EXAMPLE:

```SA = [34.7118; 34.8915; 35.0256; 34.8472; 34.7366; 34.7324;]
pt = [28.7832; 28.4209; 22.7850; 10.2305;  6.8292;  4.3245;]```
`[CT_SA, CT_pt] = gsw_CT_first_derivatives(SA,pt)`
`CT_SA =`
```  -0.041981092877806
-0.041558140199508
-0.034739209004865
-0.018711103772892
-0.014075941811725
-0.010571716552295```
`CT_pt =`
```   1.002814937296636
1.002554817053239
1.001645140295163
1.000003771100520
0.999716359504731
0.999474326580093```

## 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.12.3) and (A.12.9a,b) of this TEOS-10 Manual.```
`This software is available from http://www.TEOS-10.org`