- #1
Monsterman222
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I'm trying to figure out Ch 4, Sec. 7, Q 25.c of Mathematical Methods in the Physical Sciences, 3rd Ed. It's not homework I'm working on since I'm not in school.
Assume that [tex]f\left(x, y, z\right) = 0[/tex]
If x, y and z are each functions of t, show that
[tex]\left(\frac{\partial y}{\partial z}\right)_{x} = \left(\frac{\partial y}{\partial t} \right)_{x} / \left(\frac{\partial z}{\partial t}\right)_{x}.[/tex]
This doesn't make any sense to me. We have 4 unknowns in 4 equations, so NO independent variables. And what does it mean to say "the partial derivative of y with respect to t holding x constant", when x is a function of t only (and therefore cannot be held constant if t is changing)?
Assume that [tex]f\left(x, y, z\right) = 0[/tex]
If x, y and z are each functions of t, show that
[tex]\left(\frac{\partial y}{\partial z}\right)_{x} = \left(\frac{\partial y}{\partial t} \right)_{x} / \left(\frac{\partial z}{\partial t}\right)_{x}.[/tex]
This doesn't make any sense to me. We have 4 unknowns in 4 equations, so NO independent variables. And what does it mean to say "the partial derivative of y with respect to t holding x constant", when x is a function of t only (and therefore cannot be held constant if t is changing)?