6.19.1  Functional derivative: function_diff

The function_diff command finds the derivatives of functions (as opposed to expressions, see Section 6.15.1).

• function_diff takes one argument: f, a function.
• function_diff(f) returns the derivative f′ of f.

Examples.

• Input:
  function_diff(sin)
  Output:

  x↦ cosx

• Input:
  function_diff(sin)(x)
  Output:

  cosx

• Input:

  f(x):=x^2+x*cos(x)

  function_diff(f)

  Output:

  x↦ cosx−x sinx+2 x

• Input:
  function_diff(f)(x)
  Output:

  cosx−x sinx+2 x

• To define the function g as f′:
  Input:
  g:=function_diff(f)
• The function_diff instruction has the same effect as using the expression derivative diff (see Section 6.19.4) in conjunction with unapply (see Section 6.15.2):
  Input:

  g:=unapply(diff(f(x),x),x)

  g(x)

  Output:

  cosx−x sinx+2 x

Warning!!!
In Maple mode (see Section 3.5.2), for compatibility, D may be used in place of function_diff. For this reason, it is impossible to assign a variable named D in Maple mode (hence you can not name a geometric object D).