Given f(x, y, z) = 7x − 7y² + 6z², x = √u + v, y = (u + w) In(v), z = 2 – v + 7w. Find andofдw(Use symbolic notation and fractions where needed.)afдиafдиofдw||==of ofди, ду||

Answered: Given f(x, y, z) = 7x − 7y² + 6z², x =…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Related questions

Question

Given f(x, y, z) = 7x − 7y² + 6z², x = √u + v, y = (u + w) In(v), z = 2 – v + 7w. Find and
of
дw
(Use symbolic notation and fractions where needed.)
af
ди
af
ди
of
дw
||
=
=
of of
ди, ду
||

Expert Solution

Step 1

Firstly differentiate f with respect to x ,y ,z and then differentiate x , y , z with respect to u, v ,w and then using chain rule ,we have

$\Rightarrow \frac{\partial f}{\partial u} = \frac{\partial f}{\partial x} \frac{\partial x}{\partial u} + \frac{\partial f}{\partial y} \frac{\partial y}{\partial u} + \frac{\partial f}{\partial z} \frac{\partial z}{\partial u}, \frac{\partial f}{\partial v} = \frac{\partial f}{\partial x} \frac{\partial x}{\partial v} + \frac{\partial f}{\partial y} \frac{\partial y}{\partial v} + \frac{\partial f}{\partial z} \frac{\partial z}{\partial v}, \frac{\partial f}{\partial w} = \frac{\partial f}{\partial x} \frac{\partial x}{\partial w} + \frac{\partial f}{\partial y} \frac{\partial y}{\partial w} + \frac{\partial f}{\partial z} \frac{\partial z}{\partial w} .$