# Ejercicio 10.15

## Apartado a)

kill(all)$

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

Dxf(x,y,z) = diff(f(x,y,z),x);
Dyf(x,y,z) = diff(f(x,y,z),y);
Dzf(x,y,z) = diff(f(x,y,z),z);

## Apartado b)

kill(all)$

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

Dxf(x,y,z) = diff(f(x,y,z),x);
Dyf(x,y,z) = diff(f(x,y,z),y);
Dzf(x,y,z) = diff(f(x,y,z),z);

## Apartado c)

kill(all)$

f(x,y,z):=exp(- y^2 / (2*x))+sin(x*y) ;

Dxf(x,y,z) = diff(f(x,y,z),x);
Dyf(x,y,z) = diff(f(x,y,z),y);
Dzf(x,y,z) = diff(f(x,y,z),z);

## Apartado d)

kill(all)$

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

Dxf(x,y,z) = diff(f(x,y,z),x);
Dyf(x,y,z) = diff(f(x,y,z),y);
Dzf(x,y,z) = diff(f(x,y,z),z);