Use the Chain Rule to evaluate the partial derivative g at the point (r, 0) = (2/2, 7) where g(x, y) = 2r+5 1 x = r sin 0, y =r cos 0. %3| ag |(7,0)=(2/2, 3)

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Answer both questions. Thank you.

dg
Use the Chain Rule to evaluate the partial derivative at the point (r, 0) = (2/2, 7)
where g(x, y) = 2r+5y" >
1
x = r sin 0, y
= r cos O.
dg
|(7,0)=(2v2,3)
Transcribed Image Text:dg Use the Chain Rule to evaluate the partial derivative at the point (r, 0) = (2/2, 7) where g(x, y) = 2r+5y" > 1 x = r sin 0, y = r cos O. dg |(7,0)=(2v2,3)
Suppose z = x²
sin y, x =
2s? + 3t2, y = 6st.
A. Use the chain rule to find
dz
and
as
dz
as functions of x, y, s and t.
dz
ds
B. Find the numerical values of and when (s, t) = (3, 3).
as
dz
ds
흉 (3, 3) =D
* =
dz
(3,3)
Transcribed Image Text:Suppose z = x² sin y, x = 2s? + 3t2, y = 6st. A. Use the chain rule to find dz and as dz as functions of x, y, s and t. dz ds B. Find the numerical values of and when (s, t) = (3, 3). as dz ds 흉 (3, 3) =D * = dz (3,3)
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