Suppose z = x² sin y, x = 2s2 + 3t2, y = 4st. dz and A. Use the chain rule to find ds as functions of x, y, s and t. dz as az dz dz * when (s, t) = (1, –2). B. Find the numerical values of and ds at dz (1, –2) dz (1, –2) = 出

Suppose z = x² sin y, x = 2s2 + 3t2, y = 4st. dz and A. Use the chain rule to find ds as functions of x, y, s and t. dz as az dz dz * when (s, t) = (1, –2). B. Find the numerical values of and ds at dz (1, –2) dz (1, –2) = 出

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

Section4.4: Derivatives Of Exponential Functions

Problem 25E

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Question

Suppose z = x² sin y, x =
2s2 + 3t2, y = 4st.
dz
and
A. Use the chain rule to find
ds
as functions of x, y, s and t.
dz
as
az
dz
dz
* when (s, t) = (1, –2).
B. Find the numerical values of
and
ds
at
dz
(1, –2)
dz
(1, –2) =
出

Expert Solution

Step 1

Given:

$z = x^{2} \sin (y)$
$x = 2 s^{2} + 3 t^{2}$
$y = 4 s t$

To find:

Using chain rule,

$\frac{\partial z}{\partial s}$ and $\frac{\partial z}{\partial t}$
$\frac{\partial z}{\partial s} (1, - 2)$ and $\frac{\partial z}{\partial t} (1, - 2)$