Consider the function z(x, y), its partial derivatives

Chapter 12, Problem 4P

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QUESTION:

Problem 4P

Consider the function z(x, y), its partial derivatives (∂z/∂x)yand  (∂z/∂x)x and the total derivative dz/dx.

(a) How do the magnitudes (∂x)yand dx compare?

(b) How do the magnitudes (∂z)yand dz compare?

(c) Is there any relation among dz, (∂z)x, and (∂z)y?

Questions & Answers

QUESTION:

Problem 4P

Consider the function z(x, y), its partial derivatives (∂z/∂x)yand  (∂z/∂x)x and the total derivative dz/dx.

(a) How do the magnitudes (∂x)yand dx compare?

(b) How do the magnitudes (∂z)yand dz compare?

(c) Is there any relation among dz, (∂z)x, and (∂z)y?

ANSWER:

Step 1 of 4Given data:function,Partial derivative are , ,Total derivative is

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