Find the differential of w = ln /x² + 3y² + 2z²

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Find the differential of
In Vx2 + 3y2 + 222 .
xdx + 3ydy + 2zdz
1. dw
x² + 3y2 + 2z2
xdx + 3ydy + 2zdz
2. dw
2(x2 + 3y2 + 22²)
xdx + 3ydy + 2zdz
3. dw
Vr2 + 3y2 + 222
dx + 3dy + 2dz
x2 + 3y2 + 2z2
4. dw
dx + 3dy + 2dz
5. dw
Vx2 + 3y? + 2z²
т+ Зу + 22
6. dw
2(x2 + 3y2 + 2z?)
Transcribed Image Text:Find the differential of In Vx2 + 3y2 + 222 . xdx + 3ydy + 2zdz 1. dw x² + 3y2 + 2z2 xdx + 3ydy + 2zdz 2. dw 2(x2 + 3y2 + 22²) xdx + 3ydy + 2zdz 3. dw Vr2 + 3y2 + 222 dx + 3dy + 2dz x2 + 3y2 + 2z2 4. dw dx + 3dy + 2dz 5. dw Vx2 + 3y? + 2z² т+ Зу + 22 6. dw 2(x2 + 3y2 + 2z?)
Expert Solution
Step 1

Here we use chain rule of differentiation to find the required differential.

According to chain rule of differentiation,

      

       ddxuvx = dudxdv(x)dxsome basic formulas are,   ddxlog(x) = 1x    ddxx = 12x      dxndx = nxn-1

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