# Exercici 10.13

kill(all)$

f(x,y):=sqrt(x^2+2*y^2);

r1(t):=t$      r2(t):=2*t^2$
r(t):=[r1(t), r2(t)];

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

Jf(x,y) = Jf : jacobian([f(x,y)] , [x,y]);

'Jf(1,2) = Jf12 : subst([x=1,y=2], Jf);

Jr = Jr : matrix ( [diff(r1(t),t)] , [diff(r2(t),t)] ) ;

'a=a:[1,2]; t0=t0:1;

Tr = Tr : subst([t=1], Jr);

modul_Tr = m : sqrt(1^2+4^2);
'Tu[1]=u1: Tr/m;

Duf(1,2) = Jf12.u1;