# Ejercicio 10.14

## Apartado a)

kill(all)$

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

Derivadas parciales de primer orden

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

Derivadas parciales de segundo orden

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) );

Derivadas parciales de tercer orden

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) );

## Apartado b)

kill(all)$

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

Derivadas parciales de primer orden

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

Derivadas parciales de segundo orden

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) );

Derivadas parciales de tercer orden

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) );

## Apartado c)

kill(all)$

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

Derivadas parciales de primer orden

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

Derivadas parciales de segundo orden

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) );

Derivadas parciales de tercer orden

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) );

## Apartado d)

kill(all)$

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

Derivadas parciales de primer orden

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

Derivadas parciales de segundo orden

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) );

Derivadas parciales de tercer orden

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) );