For problems 1 through 16 find frand f for the function give

For problems 1 through 16, find frand f for the function given

Solution

f(x,y)= (x²-5y²)/(y⁴-5x²)

f_x= d/dx(x²-5y²)/(y⁴-5x⁴)

   = 2x/(y⁴-5x⁴ ) -=+ 20x³(x²-5y²)/(y⁴-5x⁴)

f_y=d/dy(x²-5y²)/(y⁴-5x⁴)   = (-10y/(y⁴-5x⁴)) +4y³(x²-5y²)/(y⁴-5x⁴)

11. f(x,y)=y⁵e^x

f_x= d/dx(y⁵e^x)= y⁵e^x

f_y=d/dy(y⁵e^x) = 5y⁴e^x