Given

Question

Given

f1(x,y)=x^4y^3
f2(x,y)=5x^7+sin(3y)

find the determinant
step plz full step

Answer 1

Do you mean the Jacobian?

F1x = 4x^3y^3
F1y = 3x^4y^2
F2x = 35x^6
F2y = 3cos(3y)

So, the determinant of J(f1,f2,x,y) is

(4x^3y^3)(3cos(3y))-(35x^6)(3x^4y^2)
= 12x^3y^3 cos(3y) - 105x^10y^2

See

http://www.wolframalpha.com/input/?i=jacobian+of+(x%5E4y%5E3,+5x%5E7%2Bsin(3y))