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

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

Advanced Engineering Mathematics
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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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 ||
Transcribed Image Text: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

⇒∂f∂u=∂f∂x∂x∂u+∂f∂y∂y∂u+∂f∂z∂z∂u ,∂f∂v=∂f∂x∂x∂v+∂f∂y∂y∂v+∂f∂z∂z∂v,∂f∂w=∂f∂x∂x∂w+∂f∂y∂y∂w+∂f∂z∂z∂w.

So ,we have 

 

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