# Christopher Walls
# Derivatives of Inverse Trigonometric Functions
# 
# This maplet does not work at present because it asks students to evaluate the derivatives at numbers outside the domain.
# 
restart;
with(Maplets):with(Maplets[Tools]):with(Maplets[Elements]):with(plots):
StartEngine();
randomize():
Derivatives:=Maplet(onstartup=RunWindow(MAIN),
Window[MAIN]('title'="Derivatives of Inverse Trig Functions",
[ halign=none,
  [ Button("New Problem", Evaluate('function'="ask")),
    HorizontalGlue(),
    Button("Quit",Shutdown()) 
  ],
  [ "Take the derivative of",
    HorizontalGlue()
  ],
  [ "f(x) =",
    MathMLViewer['question']('width'=300,'height'=60),
    HorizontalGlue()
  ],
  [ "f '(x) =", TextField['answer']('width'=40),
    HorizontalGlue()
  ],
  [ HorizontalGlue(),
    Button("Check Answer", Evaluate('function'="check")),
    HorizontalGlue(),
    Button("Show Derivative", Evaluate('function'="show")),
    HorizontalGlue()
  ],
  [ Label[Lfa]("f '(a) ="),
    TextField['answer2']('width'=40),
    HorizontalGlue()
  ],
  [ HorizontalGlue(),
    Button("Check Answer", Evaluate('function'="check2")),
    HorizontalGlue(),
    Button("Show Derivative", Evaluate('function'="show2")),
    HorizontalGlue()
  ],
  [ TextField['reply']('width'=40, 'editable'='false')
  ],
  [ "Brought to you by Chris-B-Good"
  ],
  [ "Programmer: C. Walls  Copyright P. Yasskin 2005"
  ]
]
)
):

card:=rand(0..1):
rand1:=rand(1..5):
rand3:=rand(1..6):
funcs:=[b*arcsin(a*x^n), b*arccos(a*x^n), b*arctan(a*x^n), b*arcsec(a*x^n), b*arccsc(a*x^n), b*arccot(a*x^n)];

ask:=proc()
local f,g;
global card, rand1, rand3, funcs, a, b, n, correctanswer, correctanswer2;
Set('answer'="");
Set('reply'="");
a:=(-1)^card()*rand1();
b:=(-1)^card()*rand1();
n:=rand1();
f:=funcs[rand3()];
Set('question'=MathML[Export]('f'=f));
correctanswer:=diff(f,x);
g:=rand1();
Set('Lfa'(caption)=cat("f '(", g, ") ="));
correctanswer2:=subs(x=g, correctanswer);
end proc:

check:=proc()
global correctanswer;
local useranswer;
useranswer:=Get('answer'::anything, corrections=true, update=true):
if simplify(correctanswer-useranswer=0) then
  Set('reply'="Great Googalee Mooglalee!")
else
  Set('reply'="Oops. Once more?")
end if;
end proc:
show:=proc()
global correctanswer;
Set('answer'=correctanswer);
end proc:

check2:=proc()
global correctanswer2;
local useranswer2;
useranswer2:=Get('answer2'::anything, corrections=true, update=true):
if simplify(correctanswer2-useranswer2=0) then
  Set('reply'="Wowza!")
else
  Set('reply'="So close!")
end if;
end proc:
show2:=proc()
global correctanswer2;
Set('answer2'=correctanswer2);
end proc:

Display( Derivatives );