# Exercici 10.14

## Apartat a)

kill(all)$

f(x,y):=x^4+3*x^2-4*x*y;

Derivades parcials de primer ordre

define (Dxf(x,y) , diff(f(x,y), x) );
define (Dyf(x,y) , diff(f(x,y), y) );

Derivades parcials de segon ordre

define (Dxxf(x,y) , diff(Dxf(x,y), x) );
define (Dxyf(x,y) , diff(Dxf(x,y), y) );

define (Dyxf(x,y) , diff(Dyf(x,y), x) );
define (Dyyf(x,y) , diff(Dyf(x,y), y) );

Derivades parcials de tercer ordre

define (Dxxxf(x,y) , diff(Dxxf(x,y), x) );
define (Dxxyf(x,y) , diff(Dxxf(x,y), y) );

define (Dxyxf(x,y) , diff(Dxyf(x,y), x) );
define (Dxyyf(x,y) , diff(Dxyf(x,y), y) );

define (Dyxxf(x,y) , diff(Dyxf(x,y), x) );
define (Dyxyf(x,y) , diff(Dyxf(x,y), y) );

define (Dyyxf(x,y) , diff(Dyyf(x,y), x) );
define (Dyyyf(x,y) , diff(Dyyf(x,y), y) );

## Apartat b)

kill(all)$

f(x,y):=4*x*y+x/(2*y)-(sqrt(x^2+3*y^2));

Derivades parcials de primer ordre

define (Dxf(x,y) , diff(f(x,y), x) );
define (Dyf(x,y) , diff(f(x,y), y) );

Derivades parcials de segon ordre

define (Dxxf(x,y) , diff(Dxf(x,y), x) );
define (Dxyf(x,y) , diff(Dxf(x,y), y) );

define (Dyxf(x,y) , diff(Dyf(x,y), x) );
define (Dyyf(x,y) , diff(Dyf(x,y), y) );

Derivades parcials de tercer ordre

define (Dxxxf(x,y) , diff(Dxxf(x,y), x) );
define (Dxxyf(x,y) , diff(Dxxf(x,y), y) );

define (Dxyxf(x,y) , diff(Dxyf(x,y), x) );
define (Dxyyf(x,y) , diff(Dxyf(x,y), y) );

define (Dyxxf(x,y) , diff(Dyxf(x,y), x) );
define (Dyxyf(x,y) , diff(Dyxf(x,y), y) );

define (Dyyxf(x,y) , diff(Dyyf(x,y), x) );
define (Dyyyf(x,y) , diff(Dyyf(x,y), y) );

## Apartat c)

kill(all)$

f(x,y):=%e^(-y^2/(2*x));

Derivades parcials de primer ordre

define (Dxf(x,y) , diff(f(x,y), x) );
define (Dyf(x,y) , diff(f(x,y), y) );

Derivades parcials de segon ordre

define (Dxxf(x,y) , diff(Dxf(x,y), x) );
define (Dxyf(x,y) , diff(Dxf(x,y), y) );

define (Dyxf(x,y) , diff(Dyf(x,y), x) );
define (Dyyf(x,y) , diff(Dyf(x,y), y) );

Derivades parcials de tercer ordre

define (Dxxxf(x,y) , diff(Dxxf(x,y), x) );
define (Dxxyf(x,y) , diff(Dxxf(x,y), y) );

define (Dxyxf(x,y) , diff(Dxyf(x,y), x) );
define (Dxyyf(x,y) , diff(Dxyf(x,y), y) );

define (Dyxxf(x,y) , diff(Dyxf(x,y), x) );
define (Dyxyf(x,y) , diff(Dyxf(x,y), y) );

define (Dyyxf(x,y) , diff(Dyyf(x,y), x) );
define (Dyyyf(x,y) , diff(Dyyf(x,y), y) );

## Apartat d)

kill(all)$

f(x,y):=log((x+2)/(3*sqrt(y)));

Derivades parcials de primer ordre

define (Dxf(x,y) , diff(f(x,y), x) );
define (Dyf(x,y) , diff(f(x,y), y) );

Derivades parcials de segon ordre

define (Dxxf(x,y) , diff(Dxf(x,y), x) );
define (Dxyf(x,y) , diff(Dxf(x,y), y) );

define (Dyxf(x,y) , diff(Dyf(x,y), x) );
define (Dyyf(x,y) , diff(Dyf(x,y), y) );

Derivades parcials de tercer ordre

define (Dxxxf(x,y) , diff(Dxxf(x,y), x) );
define (Dxxyf(x,y) , diff(Dxxf(x,y), y) );

define (Dxyxf(x,y) , diff(Dxyf(x,y), x) );
define (Dxyyf(x,y) , diff(Dxyf(x,y), y) );

define (Dyxxf(x,y) , diff(Dyxf(x,y), x) );
define (Dyxyf(x,y) , diff(Dyxf(x,y), y) );

define (Dyyxf(x,y) , diff(Dyyf(x,y), x) );
define (Dyyyf(x,y) , diff(Dyyf(x,y), y) );