Clear[f,x,g,h,i,d,x,xa,z,za,y,ya]
f[x_,y_,z_]:=Log[x]+(y*(z^2))*Sin[z];
g=D[f[x,y,z],x];
h=D[f[x,y,z],y];
i=D[f[x,y,z],z];

x=10;
xa=0.1;
y=234;
ya= 10;
z=2.45;
za=0.12;

d=Sqrt[g^2*xa^2+h^2*ya^2+i^2*za^2]
f[x,y,z]//N