1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
|
\begin{patch}{ExDiffBasicPatch1}
\begin{paste}{ExDiffBasicFull1}{ExDiffBasicEmpty1}
\pastebutton{ExDiffBasicFull1}{\hidepaste}
\tab{5}\spadcommand{differentiate(sin(x) * exp(x**2),x)}
\indentrel{3}\begin{verbatim}
2 2
x x
(1) 2x %e sin(x) + cos(x)%e
Type: Expression Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{ExDiffBasicEmpty1}
\begin{paste}{ExDiffBasicEmpty1}{ExDiffBasicPatch1}
\pastebutton{ExDiffBasicEmpty1}{\showpaste}
\tab{5}\spadcommand{differentiate(sin(x) * exp(x**2),x)}
\end{paste}\end{patch}
\begin{patch}{ExDiffSeveralVariablesPatch1}
\begin{paste}{ExDiffSeveralVariablesFull1}{ExDiffSeveralVariablesEmpty1}
\pastebutton{ExDiffSeveralVariablesFull1}{\hidepaste}
\tab{5}\spadcommand{differentiate(sin(x) * tan(y)/(x**2 + y**2),x)}
\indentrel{3}\begin{verbatim}
2 2
(- 2x sin(x) + (y + x )cos(x))tan(y)
(1) �������������������������������������
4 2 2 4
y + 2x y + x
Type: Expression Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{ExDiffSeveralVariablesEmpty1}
\begin{paste}{ExDiffSeveralVariablesEmpty1}{ExDiffSeveralVariablesPatch1}
\pastebutton{ExDiffSeveralVariablesEmpty1}{\showpaste}
\tab{5}\spadcommand{differentiate(sin(x) * tan(y)/(x**2 + y**2),x)}
\end{paste}\end{patch}
\begin{patch}{ExDiffSeveralVariablesPatch2}
\begin{paste}{ExDiffSeveralVariablesFull2}{ExDiffSeveralVariablesEmpty2}
\pastebutton{ExDiffSeveralVariablesFull2}{\hidepaste}
\tab{5}\spadcommand{differentiate(sin(x) * tan(y)/(x**2 + y**2),y)}
\indentrel{3}\begin{verbatim}
(2)
2 2 2
(y + x )sin(x)tan(y) - 2y sin(x)tan(y)
+
2 2
(y + x )sin(x)
/
4 2 2 4
y + 2x y + x
Type: Expression Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{ExDiffSeveralVariablesEmpty2}
\begin{paste}{ExDiffSeveralVariablesEmpty2}{ExDiffSeveralVariablesPatch2}
\pastebutton{ExDiffSeveralVariablesEmpty2}{\showpaste}
\tab{5}\spadcommand{differentiate(sin(x) * tan(y)/(x**2 + y**2),y)}
\end{paste}\end{patch}
\begin{patch}{ExDiffMultipleIPatch1}
\begin{paste}{ExDiffMultipleIFull1}{ExDiffMultipleIEmpty1}
\pastebutton{ExDiffMultipleIFull1}{\hidepaste}
\tab{5}\spadcommand{differentiate(sin(x)/(x**2 + y**2),[x,y])}
\indentrel{3}\begin{verbatim}
3 2
8x y sin(x) + (- 2y - 2x y)cos(x)
(1) ����������������������������������
6 2 4 4 2 6
y + 3x y + 3x y + x
Type: Expression Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{ExDiffMultipleIEmpty1}
\begin{paste}{ExDiffMultipleIEmpty1}{ExDiffMultipleIPatch1}
\pastebutton{ExDiffMultipleIEmpty1}{\showpaste}
\tab{5}\spadcommand{differentiate(sin(x)/(x**2 + y**2),[x,y])}
\end{paste}\end{patch}
\begin{patch}{ExDiffMultipleIPatch2}
\begin{paste}{ExDiffMultipleIFull2}{ExDiffMultipleIEmpty2}
\pastebutton{ExDiffMultipleIFull2}{\hidepaste}
\tab{5}\spadcommand{differentiate(sin(x)/(x**2 + y**2),[x,y,y])}
\indentrel{3}\begin{verbatim}
(2)
2 3 4 2 2 4
(- 40x y + 8x )sin(x) + (6y + 4x y - 2x )cos(x)
��������������������������������������������������
8 2 6 4 4 6 2 8
y + 4x y + 6x y + 4x y + x
Type: Expression Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{ExDiffMultipleIEmpty2}
\begin{paste}{ExDiffMultipleIEmpty2}{ExDiffMultipleIPatch2}
\pastebutton{ExDiffMultipleIEmpty2}{\showpaste}
\tab{5}\spadcommand{differentiate(sin(x)/(x**2 + y**2),[x,y,y])}
\end{paste}\end{patch}
\begin{patch}{ExDiffMultipleIIPatch1}
\begin{paste}{ExDiffMultipleIIFull1}{ExDiffMultipleIIEmpty1}
\pastebutton{ExDiffMultipleIIFull1}{\hidepaste}
\tab{5}\spadcommand{differentiate(cos(z)/(x**2 + y**3),[x,y,z],[1,2,3])}
\indentrel{3}\begin{verbatim}
4 3
(- 84x y + 24x y)sin(z)
(1) ��������������������������������
12 2 9 4 6 6 3 8
y + 4x y + 6x y + 4x y + x
Type: Expression Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{ExDiffMultipleIIEmpty1}
\begin{paste}{ExDiffMultipleIIEmpty1}{ExDiffMultipleIIPatch1}
\pastebutton{ExDiffMultipleIIEmpty1}{\showpaste}
\tab{5}\spadcommand{differentiate(cos(z)/(x**2 + y**3),[x,y,z],[1,2,3])}
\end{paste}\end{patch}
\begin{patch}{ExDiffHigherOrderPatch1}
\begin{paste}{ExDiffHigherOrderFull1}{ExDiffHigherOrderEmpty1}
\pastebutton{ExDiffHigherOrderFull1}{\hidepaste}
\tab{5}\spadcommand{differentiate(exp(x**2),x,4)}
\indentrel{3}\begin{verbatim}
2
4 2 x
(1) (16x + 48x + 12)%e
Type: Expression Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{ExDiffHigherOrderEmpty1}
\begin{paste}{ExDiffHigherOrderEmpty1}{ExDiffHigherOrderPatch1}
\pastebutton{ExDiffHigherOrderEmpty1}{\showpaste}
\tab{5}\spadcommand{differentiate(exp(x**2),x,4)}
\end{paste}\end{patch}
\begin{patch}{ExDiffFormalIntegralPatch1}
\begin{paste}{ExDiffFormalIntegralFull1}{ExDiffFormalIntegralEmpty1}
\pastebutton{ExDiffFormalIntegralFull1}{\hidepaste}
\tab{5}\spadcommand{f := integrate(sqrt(1 + t**3),t)\bound{f }}
\indentrel{3}\begin{verbatim}
t �������Ŀ
ڿ � 3
(1) � \�%N + 1 d%N
��
Type: Union(Expression Integer,...)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{ExDiffFormalIntegralEmpty1}
\begin{paste}{ExDiffFormalIntegralEmpty1}{ExDiffFormalIntegralPatch1}
\pastebutton{ExDiffFormalIntegralEmpty1}{\showpaste}
\tab{5}\spadcommand{f := integrate(sqrt(1 + t**3),t)\bound{f }}
\end{paste}\end{patch}
\begin{patch}{ExDiffFormalIntegralPatch2}
\begin{paste}{ExDiffFormalIntegralFull2}{ExDiffFormalIntegralEmpty2}
\pastebutton{ExDiffFormalIntegralFull2}{\hidepaste}
\tab{5}\spadcommand{differentiate(f,t)\free{f }}
\indentrel{3}\begin{verbatim}
������Ŀ
� 3
(2) \�t + 1
Type: Expression Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{ExDiffFormalIntegralEmpty2}
\begin{paste}{ExDiffFormalIntegralEmpty2}{ExDiffFormalIntegralPatch2}
\pastebutton{ExDiffFormalIntegralEmpty2}{\showpaste}
\tab{5}\spadcommand{differentiate(f,t)\free{f }}
\end{paste}\end{patch}
\begin{patch}{ExDiffFormalIntegralPatch3}
\begin{paste}{ExDiffFormalIntegralFull3}{ExDiffFormalIntegralEmpty3}
\pastebutton{ExDiffFormalIntegralFull3}{\hidepaste}
\tab{5}\spadcommand{differentiate(f * t**2,t)\free{f }}
\indentrel{3}\begin{verbatim}
t �������Ŀ ������Ŀ
ڿ � 3 2 � 3
(3) 2t � \�%N + 1 d%N + t \�t + 1
��
Type: Expression Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{ExDiffFormalIntegralEmpty3}
\begin{paste}{ExDiffFormalIntegralEmpty3}{ExDiffFormalIntegralPatch3}
\pastebutton{ExDiffFormalIntegralEmpty3}{\showpaste}
\tab{5}\spadcommand{differentiate(f * t**2,t)\free{f }}
\end{paste}\end{patch}
|
