   Chapter 14.5, Problem 17E

Chapter
Section
Textbook Problem

Use a tree diagram to write out the Chain Rule for the given case. Assume all functions are differentiable.17. u = f(x, y), where x = x(r, s, t), y = y(r, s, t)

To determine

To write: The Chain Rule for the function u=f(x,y) , where x=x(r,s,t)andy=y(r,s,t) using tree diagram.

Explanation

The given function, u=f(x,y) is differentiable.

Notice that x=x(r,s,t)andy=y(r,s,t) are the functions of r,sandt .

The tree diagram can be drawn for the given function as shown below in Figure 1.

From Figure 1, obtain the Chain Rule for ur , us and ut as follows.

ur=ux

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