Suppose z = x2 sin y, x = 3s2 + 2t2, y = 4st. A. Use the chain rule to find az and as az as functions of x, y, s and t. at az 12xs*siny+4x^2t*cosy as az = -8tx*siny+8sx^2cosy at az as when (s, t) = (-3, -2). B. Find the numerical values of and (-3, –2) = -1260sin(2y) as az (-3, -2) = -560sin(2y) at

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.
Chapter4: Calculating The Derivative
Section4.2: Derivatives Of Products And Quotients
Problem 35E
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Suppose z = x² sin y, x =
3s2 + 2t2, y = 4st.
A. Use the chain rule to find
dz
and
as
az
as functions of x, y, s and t.
at
az
12xs*siny+4x^2t*cosy
as
az
-8tx*siny+8sx^2cosy
at
az
as
dz
B. Find the numerical values of
and
when (s, t) = (-3, -2).
az
(-3, -2) = -1260sin(2y)
(-3, -2) = -560sin(2y)
as
az
at
||
Transcribed Image Text:Suppose z = x² sin y, x = 3s2 + 2t2, y = 4st. A. Use the chain rule to find dz and as az as functions of x, y, s and t. at az 12xs*siny+4x^2t*cosy as az -8tx*siny+8sx^2cosy at az as dz B. Find the numerical values of and when (s, t) = (-3, -2). az (-3, -2) = -1260sin(2y) (-3, -2) = -560sin(2y) as az at ||
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