- #1
minderbinder
- 6
- 0
Homework Statement
Show that the set defined by the equations
[tex]x + y + z + w = sin(xyzw)[/tex]
[tex]
x - y + z + w^2 = cos(xyzw) - 1[/tex]
can be described explicitly by equation of the form (z, w) = f(x, y) near the point (0,0,0,0); find the first partial derivatives of f(x,y) at the point (0,0)
Homework Equations
The above bolded part is the part I'm unsure about...
The Attempt at a Solution
I did:
[tex]
G = x + y + z + w - sin(xyzw)[/tex]
[tex]
H = x - y + z + w^2 - cos(xyzw) + 1[/tex]
[tex]
\frac{\partial (G, H)}{\partial (x, y)} + \frac{\partial (G, H)}{\partial (z, w)} \frac{\partial f}{\partial x } = 0
[/tex]
Then I solved for [tex]\frac{\partial f}{\partial x}[/tex]?