Δz=z(x_(o)+ Δx; y_(o)+ Δy)-z(x_(o);y_(o))
dz=z`_(x)(x_(o);y_(o))* Δx+z`_(y)(x_(o);y_(o))* Δy
z(x_(o)+ Δx; y_(o)+ Δy)-z(x_(o);y_(o)) ≈ z_(x)(x_(o);y_(o))* Δx+
z_(y)(x_(o);y_(o))* Δy
z(x_(o)+ Δx; y_(o)+ Δy) ≈ z(x_(o);y_(o))+z`_(x)(x_(o);y_(o))* Δx+z`_(y)(x_(o);y_(o))* Δy
z=sqrt(x^2+y^2)
x_(o)=1
y_(o)=3
Δx=0,04
Δy=0,01
z(x_(o);y_(o))=sqrt(1^2+3^2)=sqrt(10)
z`_(x)=2x/2sqrt(x^2+y^2)
z`_(y)=2y/2sqrt(x^2+y^2)
z`_(x)(x_(o);y_(o))=2*1/2sqrt(10)=1/sqrt(10)
z`_(y)(x_(o);y_(o))=2*3/2sqrt(10)=3/sqrt(10)
sqrt((1,04)^2+(3,01)^2) ≈ sqrt(10)+(1/sqrt(10))*(0,04+3*0,01)=...