Question

Oblicz pochodna czastkowa:
f(x,y)= (x^3 +y^2)/(x^2+y^2)

Answer 1

F(x,y) =(x³ + y²)/(x² + y²)
Obliczę pochodne cząstkowe I rzędu
f¹x (x,y) =[3x²(x² + y²0 - (x³ + y²)*2x]/(x² + y²)² =
= [3x⁴ +3x²y² - 2x⁴ -2xy²]/ (x² +y²)² =
=[x⁴ = 3x²y² - 2xy²]/ (x² + y²)²

f¹y (x,y) = [2y(x² + y²) -(x³ + y²)*2y] / (x² + y²)² =
= [2y(x² + y² - x³ - y²] / (x² + y²)² = [2y(x² - x³)] / (x² + y²)²