Алгоритм движения касательной по кривой

Chart1->Title->Text->Clear();
Series1->Clear();
for(x=0;x<50;x++)
{y=sin(x/10);
Series1->AddXY(x,y,"",clRed);}
for(x=0;x>-50;x--)
{y=sin(x/10);
Series1->AddXY(x,y,"",clRed);}
Chart1->Title->Text->Add("Графік синусоїди");}

double fx(double x)
{
  return x*sin(x*x)+1;
}
//---------------------------------------------------------------------------
double fdx(double x)
{
  return sin(x*x)+2*x*x*cos(x*x);
}
//---------------------------------------------------------------------------
double ftx(double x, double x0)
{
  return fx(x0)+fdx(x0)*(x-x0);
}
//---------------------------------------------------------------------------
void __fastcall TForm1::Timer1Timer(TObject *Sender)
{
// Timer1->Interval = 100;
// Timer1->Enabled = 1;
// Tag = -101;
  Refresh();
  for (double i = -1; i <= 3; i+=0.001)
    Canvas->Pixels[50*i+100][250-50*fx(i)] = clBlack;
 
  Tag++;
  if (Tag > 300)
    Tag = -101;
  double i = 1.*Tag/100.;
  if (fdx(i) > 0)
    Canvas->Pen->Color = clGreen;
  else
   if (fdx(i) < 0)
    Canvas->Pen->Color = clRed;
  else
    Canvas->Pen->Color = clBlack;
  double t = cos(ArcTan(fdx(i)));
  Canvas->MoveTo(50*(i-1*t)+100, 250-50*ftx(i-1*t, i));
  Canvas->LineTo(50*(i+1*t)+100, 250-50*ftx(i+1*t, i));
  Canvas->Pen->Color = clBlue;
  Canvas->Brush->Color = clBlue;
  Canvas->Ellipse(50*i+97, 247-50*fx(i), 50*i+103, 253-50*fx(i));
}