tests/rtest_diff_invtrig.mac

   1 (kill (all), 0);
   2 0;
   3
   4 diff(acsc(x) - asin(1/x),x);
   5 0$
   6
   7 diff(asec(x) - acos(1/x),x);
   8 0$
   9
  10 diff(asech(x) - acosh(1/x),x);
  11 0$
  12
  13 diff(acsch(x) - asinh(1/x),x);
  14 0$
  15
  16 /* A&S 4.4.9 */
  17 diff(asec(x) + acsc(x),x);
  18 0$
  19
  20 /* A&S 4.4.14 */
  21 diff(asin(-x) + asin(x),x);
  22 0$
  23
  24 /* A&S 4.4.20 */
  25 diff(asin(x) + %i*asinh(%i*x),x);
  26 0$
  27
  28 /* A&S 4.4.23 */
  29 diff(acsc(x) - %i*acsch(%i*x),x);
  30 0$
  31
  32 /* A&S 4.4.25 */
  33 diff(acot(x) - %i*acoth(%i*x),x);
  34 0$
  35
  36 /* harmonic check */
  37
  38 diff(acsc(x+%i*y),x,2) + diff(acsc(x+%i*y),y,2);
  39 0$
  40
  41 diff(asec(x+%i*y),x,2) + diff(asec(x+%i*y),y,2);
  42 0$
  43
  44 diff(acot(x+%i*y),x,2) + diff(acot(x+%i*y),y,2);
  45 0$
  46
  47 diff(asin(x+%i*y),x,2) + diff(asin(x+%i*y),y,2);
  48 0$
  49
  50 diff(acos(x+%i*y),x,2) + diff(acos(x+%i*y),y,2);
  51 0$
  52
  53 diff(atan(x+%i*y),x,2) + diff(atan(x+%i*y),y,2);
  54 0$
  55
  56 diff(acsch(x+%i*y),x,2) + diff(acsch(x+%i*y),y,2);
  57 0$
  58
  59 diff(asech(x+%i*y),x,2) + diff(asech(x+%i*y),y,2);
  60 0$
  61
  62 diff(acoth(x+%i*y),x,2) + diff(acoth(x+%i*y),y,2);
  63 0$
  64
  65 diff(asinh(x+%i*y),x,2) + diff(asinh(x+%i*y),y,2);
  66 0$
  67
  68 diff(acosh(x+%i*y),x,2) + diff(acosh(x+%i*y),y,2);
  69 0$
  70
  71 diff(atanh(x+%i*y),x,2) + diff(atanh(x+%i*y),y,2);
  72 0$