Page 113
•
Particular Partial Derivatives
1.
Find both first partial derivatives of each function:
(a)
Z ::
2x - 3y
(b)
z::
x.JY
+5
(c) z:: x 2 e2Y
(d) z:: In(x 2
+ y2)
x+y
(e) z::ln-­
x-y
x2
+ y2)
(
(f) z:: e­
•
~x2 + y2
(g)
Z=
(h)
z = tan(2x -
(i)
z = e Y sinX)'
(j) g(x,y)::
y)
y
I (t 2 - l)dt
x
2.
Find the slopes in the x and y-directions at the indicated point:
(a) g(x,y) =4 - x 2 - y2, at (1,1,2)
(b) h(x,y)
=x 2 -
y2
at (-2,1,3)
(c) z:: e- x
cosy at (0,0,1)
3.
The temperature at any point (x,y) on a steel plate is given by the function
T(x,y):: 50o-.6x 2 - 1.5y2
where x ;and y are in meters. At the point (2, 3), find the rate of change of the
temperature with respect to the distance moved along the plate in the directions of
the x andl y-axes.
•
159
Page 114
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