# Computing partial derivatives

## Problem:

Compute the partial derivatives with respect to x and y for

> f := (x,y) -> sin(sqrt(x))*log(y^2);

```                                                       2
f := (x, y) -> sin(sqrt(x)) log(y )```
 and evaluate them at (1,1/2).

 Just do it!

 w.r.t. x is fx given by

> fx := diff(f(x,y),x);

```                                         1/2      2
cos(x   ) ln(y )
fx := 1/2 ----------------
1/2
x```
 and w.r.t. y is fy given by

> fy := diff(f(x,y),y);

```                                            1/2
sin(x   )
fy := 2 ---------
y```
 For the purposes of evaluation it is more convenient to use the "D" operator. Hence, the value of the partial w.r.t. x evaluated at (1,1/2) is given by,

> D[1](f)(1.,0.5);

`                                 -.3745090200`
 and fy(1,1/2) is given by,

> Dfy := unapply(fy,(x,y));

```                                                 1/2
sin(x   )
Dfy := (x, y) -> 2 ---------
y```
 Now apply,

> Dfy(1.,0.5);

`                                  3.365883940`

Link to the commands in this file
Carlos Rodriguez <carlos@math.albany.edu>