\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)  2 x %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
        (- 2 x sin(x) + (y  + x )cos(x))tan(y)
   (1)  --------------------------------------
                    4      2 2    4
                   y  + 2 x 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)  - 2 y sin(x)tan(y)
     + 
         2    2
       (y  + x )sin(x)
  /
      4      2 2    4
     y  + 2 x 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
        8 x y sin(x) + (- 2 y  - 2 x y)cos(x)
   (1)  -------------------------------------
               6      2 4      4 2    6
              y  + 3 x y  + 3 x 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
   (- 40 x y  + 8 x )sin(x) + (6 y  + 4 x y  - 2 x )cos(x)
   -------------------------------------------------------
               8      2 6      4 4      6 2    8
              y  + 4 x y  + 6 x y  + 4 x 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
             (- 84 x y  + 24 x y)sin(z)
   (1)  -----------------------------------
         12      2 9      4 6      6 3    8
        y   + 4 x y  + 6 x y  + 4 x 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)  (16 x  + 48 x  + 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^5),t)\bound{f }}
\indentrel{3}\begin{verbatim}
           t  +-------+
         ++   |  5
   (1)   |   \|%A  + 1 d%A
        ++
                   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^5),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}
         +------+
         | 5
   (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  +-------+          +------+
            ++   |  5             2 | 5
   (3)  2 t |   \|%A  + 1 d%A  + 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}

