### Related

##### atanh-expand-integrate-log-xthru

integrate( (x-11)/(2*...

expand(xthru(derivati...

(xthru(derivative(1/2...

Calculate

##### atanh-solve-tanh

tt2: tanh( x + ((atan...

solve(tt2, y);

Calculate

atanh(3);

Calculate

##### atanh-solve

eq1: -((K/4)/atanh( (...

eq2:a*tanh(b*(2-c))+d...

eq3: a = L/2;

Calculate

fb: .1;

t1: y[n] = tanh(x[n] ...

t2: solve(t1, y[n-1]);

Calculate

##### atanh-diff-ratsimp

diff(atanh(x/2), x), ...

Calculate

##### atanh-solve

eq1: -((K/4)/atanh( (...

eq2:a*tanh(b*(2-c))+d...

eq3: a = L/2;

Calculate

##### atanh-expand-integrate-log-xthru

integrate( (x-11)/(2*...

integrate( 1/x, x);

expand(xthru(derivati...

Calculate

##### atanh-integrate

integrate(atanh(x), x);

Calculate

##### atanh-linsolve-tan

eq1:(ln(tan(x/2)+sqrt...

eq2: sqrt2atanh((1/2*...

linsolve([eq1,eq2],[x...

Calculate

### atanh

Run Example
```(%i1)a:1;
(%o1)                                  1
(%i2) b:sqrt(2);
(%o2)                               sqrt(2)
(%i3) diff(asin(x),x) ;
1
(%o3)                            ------------
2
sqrt(1 - x )
(%i4) diff(acos(x),x) ;
1
(%o4)                           - ------------
2
sqrt(1 - x )
(%i5) diff(atan(x),x) ;
1
(%o5)                               ------
2
x  + 1
(%i6) c:diff(asin(x)+acos(x),x);
(%o6)                                  0
(%i7) taylor(cos(x),x,0,5) ;
2    4
x    x
(%o7)/T/                      1 - -- + -- + . . .
2    24
(%i8) taylor(log(1+x)/sin(x),x,0,5) ;
2    3       4        5
x   x    x    11 x    157 x
(%o8)/T/           1 - - + -- - -- + ----- - ------ + . . .
2   2    3     40      720
(%i9) taylor(atanh(x),x,0,4) ;
3
x
(%o9)/T/                        x + -- + . . .
3
(%i10) limit((1+(1/n))^n,n,inf);
(%o10)                                %e
(%i11) ```
Run Example
```diff(atanh(x/2), x), ratsimp;
2
(%o1)                              - ------
2
x  - 4
(%i2) ```
Run Example
```fb: .1;
(%o1)                                 0.1
(%i2) t1: y[n] = tanh(x[n] + y[n-1] * fb);
(%o2)                     y  = tanh(x  + 0.1 y     )
n         n        n - 1
(%i3) t2: solve(t1, y[n-1]);

rat: replaced 0.1 by 1/10 = 0.1
(%o3)                   [y      = 10 atanh(y ) - 10 x ]
n - 1             n        n
(%i4) t3: 10*atanh(y[n]) - 10*x[n];
(%o4)                        10 atanh(y ) - 10 x
n        n
(%i5) solve(t2, y[n]);
y
n - 1
(%o5)                      [y  = tanh(x  + ------)]
n         n     10