Method on @symfun: diff (f) ¶

Method on @symfun: diff (f, x) ¶

Method on @symfun: diff (f, x, x, …) ¶

Method on @symfun: diff (f, x, n) ¶

Method on @symfun: diff (f, x, y) ¶

Method on @symfun: diff (f, x, x, y, y, …) ¶

Method on @symfun: diff (f, x, n, y, m, …) ¶

Symbolic differentiation of symbolic functions.

Mostly the same as @sym/diff (and indeed it calls that code) but returns a symfun.

The derivative is itself a symfun so you can evaluate at a point like:

syms u(x)
up = diff(u)           % u'(x)
  ⇒ up(x) = (symfun)
      d
      ──(u(x))
      dx
up(2)                  % u'(2)
  ⇒ ans = (sym)
      ⎛d       ⎞│
      ⎜──(u(x))⎟│
      ⎝dx      ⎠│x=2

On GNU Octave, a further shortcut is possible:

syms u(x)
diff(u)(2)
  ⇒ ans = (sym)
      ⎛d       ⎞│
      ⎜──(u(x))⎟│
      ⎝dx      ⎠│x=2

syms f(x, y)
diff(f, x, y, y)(3, 2)     % a third partial eval at (3, 2)
  ⇒ ans = (sym)
      ⎛   3           ⎞│
      ⎜  ∂            ⎟│
      ⎜──────(f(x, y))⎟│
      ⎜  2            ⎟│
      ⎝∂y  ∂x         ⎠│x=3, y=2

See also: @@sym/diff, @@symfun/int.

Package: symbolic