#! /usr/bin/env python3
#
def sympy_derivative ( ):

#*****************************************************************************80
#
## sympy_derivative() uses sympy() to evaluate derivatives.
#
#  Licensing:
#
#    This code is distributed under the MIT license. 
#
#  Modified:
#
#    01 August 2024
#
#  Author:
#
#    John Burkardt
#
  print ( '' )
  print ( 'sympy_derivative():' )
  print ( '  Demonstrate the computation of derivatives.' )
  print ( '' )

  derivative_humps ( )
  derivative_x_exp_xt ( )
#
#  Terminate.
#
  print ( '' )
  print ( 'sympy_derivative():' )
  print ( '  Normal end of execution.' )
  print ( '' )

  return

def derivative_humps ( ):

#*****************************************************************************80
#
## derivative_humps() differentiates humps(x)
#
#  Licensing:
#
#    This code is distributed under the MIT license. 
#
#  Modified:
#
#    01 August 2024
#
#  Author:
#
#    John Burkardt
#
  from sympy import diff
  from sympy import symbols

  print ( '' )
  print ( 'derivative_humps():' )
  print ( '  Differentiate humps(x).' )

  x = symbols ( 'x' )

  humps = 100 / ( ( 10 * x - 3 )**2 + 1 ) \
        + 100 / ( ( 10 * x - 9 )**2 + 4 ) \
        - 6

  print ( '' )
  print ( '  humps(x) = ', humps )

  dhumpsdx = diff ( humps, x )
  print ( '  d humps /dx = ', dhumpsdx )

  d2humpsdx2 = diff ( humps, x, 2 )
  print ( '  d2 humps /dx2 = ', d2humpsdx2 )

  return

def derivative_x_exp_xt ( ):

#*****************************************************************************80
#
## derivative_x_exp_xt() differentiates x exp(xt).
#
#  Licensing:
#
#    This code is distributed under the MIT license. 
#
#  Modified:
#
#    01 August 2024
#
#  Author:
#
#    John Burkardt
#
  from sympy import diff
  from sympy import exp
  from sympy import symbols

  print ( '' )
  print ( 'derivative_x_exp_xt():' )
  print ( '  Differentiate z(x,t) = x*exp(x*t).' )

  x = symbols ( 'x' )
  t = symbols ( 't' )
  z = x * exp ( x * t )

  print ( '' )
  print ( '  z(x,t) = ', z )
  dzdx = diff ( z, x )
  print ( '  dzdx = ', dzdx )
  dzdt = diff ( z, t )
  print ( '  dzdt = ', dzdt )
  dz2dt2 = diff ( z, t, 2 )
  print ( '  d2zdt2 = ', dz2dt2 )
  dz2dtdx = diff ( z, t, x )
  print ( '  d2zdtdx = ', dz2dtdx )

  return

if ( __name__ == "__main__" ):
  sympy_derivative ( )