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y=1/4*(ln*(x-1)/(x+1))-1/2arctgx
Derivada de la función/ y=1/4*(ln*(x-1)/(x+1))-1/2arctgx

Derivada de y=1/4*(ln*(x-1)/(x+1))-1/2arctgx

Función f() - derivada -er orden en el punto
v

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src] 
/log(x - 1)\          
|----------|          
\  x + 1   /   acot(x)
------------ - -------
     4            2
−acot⁡(x)2+1x+1log⁡(x−1)4- \frac{\operatorname{acot}{\left(x \right)}}{2} + \frac{\frac{1}{x + 1} \log{\left(x - 1 \right)}}{4} 
(log(x - 1)/(x + 1))/4 - acot(x)/2
Gráfica
02468-8-6-4-2-10102-2
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
    1        log(x - 1)           1        
---------- - ---------- + -----------------
  /     2\            2   4*(x + 1)*(x - 1)
2*\1 + x /   4*(x + 1)
12(x2+1)−log⁡(x−1)4(x+1)2+14(x−1)(x+1)\frac{1}{2 \left(x^{2} + 1\right)} - \frac{\log{\left(x - 1 \right)}}{4 \left(x + 1\right)^{2}} + \frac{1}{4 \left(x - 1\right) \left(x + 1\right)}
Simplificar
Segunda derivada [src] 
log(-1 + x)       x                1                     1         
----------- - --------- - ------------------- - -------------------
          3           2            2                              2
 2*(1 + x)    /     2\    2*(1 + x) *(-1 + x)   4*(1 + x)*(-1 + x) 
              \1 + x /
−x(x2+1)2+log⁡(x−1)2(x+1)3−12(x−1)(x+1)2−14(x−1)2(x+1)- \frac{x}{\left(x^{2} + 1\right)^{2}} + \frac{\log{\left(x - 1 \right)}}{2 \left(x + 1\right)^{3}} - \frac{1}{2 \left(x - 1\right) \left(x + 1\right)^{2}} - \frac{1}{4 \left(x - 1\right)^{2} \left(x + 1\right)}
Simplificar
Tercera derivada [src] 
                                          2                                                               
      1                1               4*x      3*log(-1 + x)            3                     3          
- --------- + ------------------- + --------- - ------------- + ------------------- + --------------------
          2                     3           3              4             3                     2         2
  /     2\    2*(1 + x)*(-1 + x)    /     2\      2*(1 + x)     2*(1 + x) *(-1 + x)   4*(1 + x) *(-1 + x) 
  \1 + x /                          \1 + x /
4x2(x2+1)3−1(x2+1)2−3log⁡(x−1)2(x+1)4+32(x−1)(x+1)3+34(x−1)2(x+1)2+12(x−1)3(x+1)\frac{4 x^{2}}{\left(x^{2} + 1\right)^{3}} - \frac{1}{\left(x^{2} + 1\right)^{2}} - \frac{3 \log{\left(x - 1 \right)}}{2 \left(x + 1\right)^{4}} + \frac{3}{2 \left(x - 1\right) \left(x + 1\right)^{3}} + \frac{3}{4 \left(x - 1\right)^{2} \left(x + 1\right)^{2}} + \frac{1}{2 \left(x - 1\right)^{3} \left(x + 1\right)}
Simplificar
Gráfico
Derivada de y=1/4*(ln*(x-1)/(x+1))-1/2arctgx
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