Unformatted text preview: So a bunch of people have been asking me why they’re getting:
∂z
∂x y ∂x
∂y z ∂y
∂z =1
x I probably said in class that one could do the following:
∂x
∂y =
z ∂x
∂z ∂z
∂y y x The problem here is that there’s nothing on the right hand side that says that
we’re actually holding z constant. When I had derived the Euler chain rule I
did the following:
∂z
∂z
dz =
dx +
dy = 0
∂x y
∂y x
We can state that z is unchanging by setting dz = 0. Then we can move stuﬀ
around.
∂z
∂x
dx
=−
dy ∂z
∂y dx = −
y x ∂y
∂z ∂z
∂y
= y dy
x ∂x
∂y z Since there is no z and we are holding it constant manually, (∂x/∂y )z = dx/dy .
As you can see, now there’s a −1 present. Crazy huh? 1 ...
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 Fall '08
 Raineri,F
 Calculus, Physical chemistry, Derivative, pH, Following, ∂z, Righthand rule

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