FICHA 02

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Ficha 02 
1. Z = 5xy – x² 
 
 
 
 
 
 
 
 
2. f(x, y) = x² + y² – 10 
 
fx = 2x fy = 2y 
 
3. Z = 2x + 5y – 3 
 
 
 
 
 
 
 
 
4. Z = 
 
f´(u) . u´ 
 
Z = Z = 
 u = xy u = xy 
 ux´ = y uy´ = x 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
5. f(x, y) = x²y + 3y² 
 
fx = 2xy fy = x² + 6y 
 
6. f(x, y) = 
 
 
 
 
 
fx = fy = 
 u = x²y u = x²y 
 ux´ = 2xy uy´= x² 
 
fx = 
 fy = 
 
 
 
7. f(x, y) = xcos(y – x) 
 
fx = 
fx = cos (y – x) + xsen(y – x) 
 
fy = 
fy = –xsen(y – x) 
 
8. f(x, y, z) = xy + yz + xz 
 
fx = y + z fy = x + y fz = y + x 
 
9. f(x, y, z) = yzln(xy) 
 
fx = yzln(u) fy = yzln(u) fz = yln(xy) 
 u = xy u = xy 
 ux´ = y uy´ = x 
 
fx = 
 
 
 fy = 
 
 
 
 
fx = 
 
 
 fy = zln(xy) + 
 
 
 
 
fy = zln(xy) + z 
 
10. f(x, y, z) = 
 
fx = fy = fz = 
 u = –x² –y² –z² u = –x² –y² –z² u = –x² –y² –z² 
 ux´ = –2x uy´ = –2y ux´ = –2z 
 
fx = –2x fy = –2y fz = –2z 
 
11. a) Z = x² – 3y³ + 4x²y² 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
b) Z =x²y² − xy 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 c) Z = ln(xy) 
 
 
 
 
 
 
 
u = xy u = xy 
 ux´ = y uy´ = x 
 
 
 
 
 
 
 = 
 
 
 
 
 
 
 
 
 = 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 d) Z = 
 
 
 
 = 
 
 
 = 
 u = xy u = xy 
 ux´ = y uy´ = x 
 
 
 
 
 = 
 
 
 = 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
12. Z = x + y + x³ − x² − y² 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
13. Z = xcos(xy)