Ok, the problem is Suppose F(x,y,z)=0 implicitly defines each of the three variables x,y, and z as functions of the other two: z=f(x,y) , y=g(x,z) x=h(y,z). If F is differentiable and F sub x, F sub y and F sub z are all non-zero, show that
partial of z with respect to x times the partial of x with respect to y times the partial of y with respect to z = -1
I am so lost. I made my tree as follows, but I guess I don't know how to get started from there.
F
/ | \
z y x
/ \ / \ / \
x y x z y z
If someone could help me get started I would greatly appreciate it!
partial of z with respect to x times the partial of x with respect to y times the partial of y with respect to z = -1
I am so lost. I made my tree as follows, but I guess I don't know how to get started from there.
F
/ | \
z y x
/ \ / \ / \
x y x z y z
If someone could help me get started I would greatly appreciate it!