nanni (arn437) – Assignment 17 – guntel – (54940)
1
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7
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001
10.0points
Determine
f
x
when
f
(
x, y
) =
x
sin(
x
+ 2
y
) + cos(
x
+ 2
y
)
.
1.
f
x
= 2 cos(
x
+ 2
y
)

x
sin(
x
+ 2
y
)
2.
f
x
=

2
x
sin(
x
+ 2
y
)
3.
f
x
=
x
cos(
x
+ 2
y
)
correct
4.
f
x
= 2 sin(
x
+ 2
y
) +
x
cos(
x
+ 2
y
)
5.
f
x
=

x
sin(
x
+ 2
y
)
6.
f
x
= 2 cos(
x
+ 2
y
) +
x
sin(
x
+ 2
y
)
7.
f
x
= 2
x
cos(
x
+ 2
y
)
8.
f
x
= 2 sin(
x
+ 2
y
)

x
cos(
x
+ 2
y
)
Explanation:
From the Product Rule we see that
f
x
= sin(
x
+2
y
)+
x
cos(
x
+2
y
)

sin(
x
+2
y
)
.
Consequently,
f
x
=
x
cos(
x
+ 2
y
)
.
002
10.0points
Find the slope in the
x
direction at the
point (1,

2, 2) on the graph of
f
when
f
(
x,y
) =
xy
2
+
x
2
y.
Correct answer: 0.
Explanation:
The graph of
f
is a surface in 3space and
the slope in the
x
direction at the point (1,

2,
2) on that surface is the value of the partial
derivative
f
x
at (1
,

2). Now
f
x
=
y
2
+ 2
xy,
so
f
x
vextendsingle
vextendsingle
vextendsingle
(1
,

2)
= 0
.
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 Fall '10
 Gualdini
 Calculus, Derivative, fxy, fxx

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