Example 4: w=x²y+y+xz_x= cos(0) y=sin(0) z=0² dw Find dt

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter6: Applications Of The Derivative
Section6.CR: Chapter 6 Review
Problem 38CR
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Example 4: w= x²y+y+xz_x = cos(0) y=sin(0) z=02
dw
Find dt
Several independent variables
z = f(x,y) and x = x(s,t) y = y(s,t)
- Əz
Əz ax Əz ay
+
as
дх as
ду дя
Əz дл ax Əz ἂν
=
+
at дх at ду at
Example 5: z = 3x² - y²
дл
Əz
Where x = 2s + 7t and y = 5st Find as
at
Example 6 Draw diagrams and write the corresponding
formuli
w( x(s,t,r), y(s,t), z( t))
Transcribed Image Text:Example 4: w= x²y+y+xz_x = cos(0) y=sin(0) z=02 dw Find dt Several independent variables z = f(x,y) and x = x(s,t) y = y(s,t) - Əz Əz ax Əz ay + as дх as ду дя Əz дл ax Əz ἂν = + at дх at ду at Example 5: z = 3x² - y² дл Əz Where x = 2s + 7t and y = 5st Find as at Example 6 Draw diagrams and write the corresponding formuli w( x(s,t,r), y(s,t), z( t))
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