Chain Rule & PDES: Solving ∂z/∂u

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SUMMARY

The discussion focuses on applying the chain rule to compute the derivative ∂z/∂u, where z is a function of x and y, with y being a function of x and x being a function of u and v. The correct formulation of the chain rule in this context is given by the equation ∂z/∂u = (∂z/∂x)(∂x/∂u) + (∂z/∂y)(dy/dx)(∂x/∂u). The user expresses difficulty in visualizing the dependencies, suggesting that a diagram may aid in understanding the relationships between the variables.

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Kork
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Im new on the forum, so I hope you guys will have some patience with me :-)

I have a question about the chain rule and partial differential equations that I can't solve, it's:

Write the appropriate version of the chain rule for the derivative:

∂z/∂u if z=g(x,y), where y=f(x) and x=h(u,v)

I have tried to do a dependence chart of it, but it's just not working for me.

Thank you very much.
 
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∂z/∂u=(∂z/∂x)(∂x/∂u)+(∂z/∂y)(dy/dx)(∂x/∂u)

Draw a diagram. It is pretty straightforward.
 

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