csch;

Calculate

? csch;

Calculate

csch;

Calculate

? csch;

Calculate

### csch

Run Example
```(%i1)diff(coth(cos(asinh(acosh(csch(sqrt(x+(1/x))))))),x,2);
1  2     2          1       2          1
(%o1) ((1 - --)  coth (sqrt(x + -)) csch (sqrt(x + -))
2                  x                  x
x
2                           1
sin (asinh(acosh(csch(sqrt(x + -))))) coth(cos(asinh(acosh(csch(sqrt(x
x
1           2                               1
+ -)))))) csch (cos(asinh(acosh(csch(sqrt(x + -)))))))
x                                           x
1       2          1              2               1
/(2 (x + -) (csch (sqrt(x + -)) - 1) (acosh (csch(sqrt(x + -))) + 1))
x                  x                              x
1  2     3          1                                 1
+ ((1 - --)  csch (sqrt(x + -)) sin(asinh(acosh(csch(sqrt(x + -)))))
2                  x                                 x
x
2                               1
csch (cos(asinh(acosh(csch(sqrt(x + -)))))))
x
1           2          1                  2               1
/(4 (x + -) sqrt(csch (sqrt(x + -)) - 1) sqrt(acosh (csch(sqrt(x + -))) + 1))
x                      x                                  x
1  2     2          1                 1
+ ((1 - --)  coth (sqrt(x + -)) csch(sqrt(x + -))
2                  x                 x
x
1          2
sin(asinh(acosh(csch(sqrt(x + -))))) csch (cos(asinh(acosh(csch(sqrt(x
x
1                1           2          1                  2               1
+ -)))))))/(4 (x + -) sqrt(csch (sqrt(x + -)) - 1) sqrt(acosh (csch(sqrt(x + -)))
x                x                      x                                  x
+ 1))
1                 1                                 1
- (coth(sqrt(x + -)) csch(sqrt(x + -)) sin(asinh(acosh(csch(sqrt(x + -)))))
x                 x                                 x
2                               1
csch (cos(asinh(acosh(csch(sqrt(x + -)))))))
x
3          1           2          1                  2               1
/(x  sqrt(x + -) sqrt(csch (sqrt(x + -)) - 1) sqrt(acosh (csch(sqrt(x + -))) + 1))
x                      x                                  x
1  2               1                 1
+ ((1 - --)  coth(sqrt(x + -)) csch(sqrt(x + -))
2                 x                 x
x
1          2
sin(asinh(acosh(csch(sqrt(x + -))))) csch (cos(asinh(acosh(csch(sqrt(x
x
1                1 3/2          2          1                  2               1
+ -)))))))/(4 (x + -)    sqrt(csch (sqrt(x + -)) - 1) sqrt(acosh (csch(sqrt(x + -)))
x                x                         x                                  x
+ 1))
1  2     2          1       3          1
- ((1 - --)  coth (sqrt(x + -)) csch (sqrt(x + -))
2                  x                  x
x
1          2
sin(asinh(acosh(csch(sqrt(x + -))))) csch (cos(asinh(acosh(csch(sqrt(x
x
1                1       2          1       3/2           2               1
+ -)))))))/(4 (x + -) (csch (sqrt(x + -)) - 1)    sqrt(acosh (csch(sqrt(x + -)))
x                x                  x                                     x
+ 1))
1  2     2          1       2          1                       1
- ((1 - --)  coth (sqrt(x + -)) csch (sqrt(x + -)) acosh(csch(sqrt(x + -)))
2                  x                  x                       x
x
1          2
sin(asinh(acosh(csch(sqrt(x + -))))) csch (cos(asinh(acosh(csch(sqrt(x
x
1                1       2          1
+ -)))))))/(4 (x + -) (csch (sqrt(x + -)) - 1)
x                x                  x
2               1        3/2
(acosh (csch(sqrt(x + -))) + 1)   )
x
1  2     2          1       2          1
+ ((1 - --)  coth (sqrt(x + -)) csch (sqrt(x + -))
2                  x                  x
x
1          2
cos(asinh(acosh(csch(sqrt(x + -))))) csch (cos(asinh(acosh(csch(sqrt(x
x
1                1       2          1              2               1
+ -)))))))/(4 (x + -) (csch (sqrt(x + -)) - 1) (acosh (csch(sqrt(x + -)))
x                x                  x                              x
+ 1))
(%i2) ```
Run Example
```residue (((csc(z)*csch(z))/(z^3)), z, 0);
1
(%o1)                                 --
90
(%i2)  residue (sin(a*x)/x**4, x, 0);
3
a
(%o2)                                - --
6
(%i3) ```
Run Example
```display2d=false;
(%o1)                            true = false
(%i2) (diff(coth(cos(arcsinh(arccosh(csch(sqrt(x+(1/x))))))),x,2));
2                               1
(%o2) 2 sin (arcsinh(arccosh(csch(sqrt(x + -)))))
x
d                                 1      2
(-- (arcsinh(arccosh(csch(sqrt(x + -))))))
dx                                x
1
coth(cos(arcsinh(arccosh(csch(sqrt(x + -))))))
x
2                                   1
csch (cos(arcsinh(arccosh(csch(sqrt(x + -))))))
x
1
+ sin(arcsinh(arccosh(csch(sqrt(x + -)))))
x
2
d                                  1
(--- (arcsinh(arccosh(csch(sqrt(x + -))))))
2                                x
dx
2                                   1
csch (cos(arcsinh(arccosh(csch(sqrt(x + -))))))
x
1
+ cos(arcsinh(arccosh(csch(sqrt(x + -)))))
x
d                                 1      2
(-- (arcsinh(arccosh(csch(sqrt(x + -))))))
dx                                x
2                                   1
csch (cos(arcsinh(arccosh(csch(sqrt(x + -))))))
x
(%i3) ```

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