HW 07 (1291626)
Due:
Thu Jun 17 2010 11:59 PM CDT
Question
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Description
15.5 The chain rule 15.6 Directional derivatives and the gradient vector
SCalc6 15.5.001. [1315822]
1.
Question Details
Use the Chain Rule to find
dz
/
dt
. (Enter your answer only in terms of
t
.)
z
=
x
2
+
y
2
+
xy
,
x
= sin(
t
),
y
=
e
t
dz
/
dt
=
SCalc6 15.5.002. [1281599]
2.
Question Details
Use the Chain Rule to find
dz
/
dt
. (Enter your answer only in terms of
t
.)
z
=
cos
(
x
+
2
y
),
x
=
8
t
2
,
y
=
6
/
t
dz
/
dt
=
SCalc6 15.5.005. [1280699]
3.
Question Details
Use the Chain Rule to find
dw
/
dt
. (Enter your answer only in terms of
t
.)
w
=
xe
y /z
,
x
=
t
2
,
y
=
7

t
, z =
9
+
2
t
dw
/
dt
=
SCalc6 15.5.008. [1279976]
4.
Question Details
Page 1 of 7
Assignment Previewer
6/10/2010
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View Full DocumentUse the Chain Rule to find
∂
z
/
∂
s
and
∂
z
/
∂
t
. (Enter your answer only in terms of
s
and
t
.)
z
= arcsin(
x

y
),
x
=
s
2
+
t
2
,
y
=
3

4
st
∂
z
/
∂
s
=
∂
z
/
∂
t
=
SCalc6 15.5.011. [1281690]
5.
Question Details
Use the Chain Rule to find
∂
z
/
∂
s
and
∂
z
/
∂
t
. (Enter your answer only in terms of
s
and
t
.)
z
=
e
r
cos
(
θ
),
r
=
st
,
θ
=
∂
z
/
∂
s
=
∂
z
/
∂
t
=
SCalc6 15.5.015. [832540]
6.
Question Details
Suppose
f
is a differentiable function of
x
and
y
, and
g
(
u, v
) =
f
(
e
u
+ sin(
v
),
e
u
+ cos(
v
)). Use the table of values to calculate
g
u
(
0
,
0
)
and
g
v
(
0
,
0
).
g
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 Summer '10
 mccray
 Chain Rule, Derivative, The Chain Rule, Vector Calculus, Assignment Previewer, Question DetailsSCalc6

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