(kill (all), 0);
0;

diff(acsc(x) - asin(1/x),x);
0$

diff(asec(x) - acos(1/x),x);
0$

diff(asech(x) - acosh(1/x),x);
0$

diff(acsch(x) - asinh(1/x),x);
0$

/* A&S 4.4.9 */
diff(asec(x) + acsc(x),x);
0$

/* A&S 4.4.14 */
diff(asin(-x) + asin(x),x);
0$

/* A&S 4.4.20 */
diff(asin(x) + %i*asinh(%i*x),x);
0$

/* A&S 4.4.23 */
diff(acsc(x) - %i*acsch(%i*x),x);
0$

/* A&S 4.4.25 */
diff(acot(x) - %i*acoth(%i*x),x);
0$

/* harmonic check */

diff(acsc(x+%i*y),x,2) + diff(acsc(x+%i*y),y,2);
0$

diff(asec(x+%i*y),x,2) + diff(asec(x+%i*y),y,2);
0$

diff(acot(x+%i*y),x,2) + diff(acot(x+%i*y),y,2);
0$

diff(asin(x+%i*y),x,2) + diff(asin(x+%i*y),y,2);
0$

diff(acos(x+%i*y),x,2) + diff(acos(x+%i*y),y,2);
0$

diff(atan(x+%i*y),x,2) + diff(atan(x+%i*y),y,2);
0$

diff(acsch(x+%i*y),x,2) + diff(acsch(x+%i*y),y,2);
0$

diff(asech(x+%i*y),x,2) + diff(asech(x+%i*y),y,2);
0$

diff(acoth(x+%i*y),x,2) + diff(acoth(x+%i*y),y,2);
0$

diff(asinh(x+%i*y),x,2) + diff(asinh(x+%i*y),y,2);
0$

diff(acosh(x+%i*y),x,2) + diff(acosh(x+%i*y),y,2);
0$

diff(atanh(x+%i*y),x,2) + diff(atanh(x+%i*y),y,2);
0$
