Question

Let $z=f(x-y, y-x) .$ Show that $\partial z / \partial x+\partial z / \partial y=0$.

Name: Let z=f(x-y, y-x) . Show that ∂ z / ∂ x+∂ z / ∂ y=0.
Uploaded: 2023-08-16T18:37:24-08:00
Duration: 2 min 47 s
Channel: Madhur L
Description: Let z=f(x-y, y-x) . Show that ∂ z / ∂ x+∂ z / ∂ y=0.

          Let $z=f(x-y, y-x) .$ Show that $\partial z / \partial x+\partial z / \partial y=0$.

Added by Andrew E.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur L

08/16/2023

Step 1

Using the chain rule, we have: $\frac{\partial z}{\partial x} = \frac{\partial f}{\partial (x-y)} \cdot \frac{\partial (x-y)}{\partial x} + \frac{\partial f}{\partial (y-x)} \cdot \frac{\partial (y-x)}{\partial x}$ $\frac{\partial z}{\partial y} = Show more…

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