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Cell[CellGroupData[{Cell[TextData["Derivatives"], "Section",
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Cell[TextData[{
  "This notebook gives a brief explanation of how to use ",
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  "  to take derivatives and to apply the chain rule properly.  See the ",
  StyleBox["Mathematica",
    FontSlant->"Italic"],
  "  book for more details."
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Cell[CellGroupData[{Cell[TextData["Ordinary Derivatives"], "Subsection",
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Cell[TextData[{
  "The built in function ",
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  " also calculates the derivative"
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  "With the function ",
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  "The function ",
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  " can be used to calculate partial derivatives. "
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  ":"
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  "Mixed partial derivatives with respect to ",
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    FontWeight->"Bold"],
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  "Such abbreviations can be combined. For example, 3 partial derivatives \
with respect to ",
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  " and 2 with respect to ",
  StyleBox["y",
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Cell[CellGroupData[{Cell[TextData["Chain Rule"], "Subsection",
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Cell[TextData[{
  "The function ",
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  " will automatically apply the chain rule properly if the dependencies \
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3 x[t]  y[t]  x'[t] - y'[t] + 2 x[t]  y[t] y'[t]\
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Cell[TextData[{
  "Notice that ",
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  " and give ",
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  "  to complete the expression for the derivative."
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 (1,0)                  (1,0)
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 (0,1)                  (0,1)
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  "Notice that the partial derivatives of ",
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Cell[TextData[{
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  ""
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information about how the variables depend on each other so that the partial \
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  ", and ",
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  " can be computed as follows:"
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