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y=tanh^-1(1-2x)
Derivada de la función/ y=tan/ y=tanh^-1(1-2x)

Derivada de y=tanh^-1(1-2x)

Función f() - derivada -er orden en el punto
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Gráfico:

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Solución

Ha introducido [src] 
      1      
-------------
tanh(1 - 2*x)
1tanh⁡(1−2x)\frac{1}{\tanh{\left(1 - 2 x \right)}} 
1/tanh(1 - 2*x)
Gráfica
02468-8-6-4-2-1010-2000020000
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Trazar el gráfico f'(x)
Primera derivada [src] 
          2         
2 - 2*tanh (1 - 2*x)
--------------------
       2            
   tanh (1 - 2*x)
2−2tanh⁡2(1−2x)tanh⁡2(1−2x)\frac{2 - 2 \tanh^{2}{\left(1 - 2 x \right)}}{\tanh^{2}{\left(1 - 2 x \right)}}
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Segunda derivada [src] 
  /             2          \                       
  |    -1 + tanh (-1 + 2*x)| /         2          \
8*|1 - --------------------|*\-1 + tanh (-1 + 2*x)/
  |          2             |                       
  \      tanh (-1 + 2*x)   /                       
---------------------------------------------------
                   tanh(-1 + 2*x)
8(−tanh⁡2(2x−1)−1tanh⁡2(2x−1)+1)(tanh⁡2(2x−1)−1)tanh⁡(2x−1)\frac{8 \left(- \frac{\tanh^{2}{\left(2 x - 1 \right)} - 1}{\tanh^{2}{\left(2 x - 1 \right)}} + 1\right) \left(\tanh^{2}{\left(2 x - 1 \right)} - 1\right)}{\tanh{\left(2 x - 1 \right)}}
Simplificar
Tercera derivada [src] 
   /                                                3                           2\
   |                          /         2          \      /         2          \ |
   |          2             3*\-1 + tanh (-1 + 2*x)/    5*\-1 + tanh (-1 + 2*x)/ |
16*|2 - 2*tanh (-1 + 2*x) - ------------------------- + -------------------------|
   |                                 4                           2               |
   \                             tanh (-1 + 2*x)             tanh (-1 + 2*x)     /
16(−3(tanh⁡2(2x−1)−1)3tanh⁡4(2x−1)+5(tanh⁡2(2x−1)−1)2tanh⁡2(2x−1)−2tanh⁡2(2x−1)+2)16 \left(- \frac{3 \left(\tanh^{2}{\left(2 x - 1 \right)} - 1\right)^{3}}{\tanh^{4}{\left(2 x - 1 \right)}} + \frac{5 \left(\tanh^{2}{\left(2 x - 1 \right)} - 1\right)^{2}}{\tanh^{2}{\left(2 x - 1 \right)}} - 2 \tanh^{2}{\left(2 x - 1 \right)} + 2\right)
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Gráfico
Derivada de y=tanh^-1(1-2x)
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