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y=thx-((1/3)th^3x)

Derivada de y=thx-((1/3)th^3x)

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Solución

Ha introducido [src]
              3   
          tanh (x)
tanh(x) - --------
             3    
$$- \frac{\tanh^{3}{\left(x \right)}}{3} + \tanh{\left(x \right)}$$
tanh(x) - tanh(x)^3/3
Gráfica
Primera derivada [src]
                   2    /          2   \
        2      tanh (x)*\3 - 3*tanh (x)/
1 - tanh (x) - -------------------------
                           3            
$$- \frac{\left(3 - 3 \tanh^{2}{\left(x \right)}\right) \tanh^{2}{\left(x \right)}}{3} - \tanh^{2}{\left(x \right)} + 1$$
Segunda derivada [src]
  /         2   \ /          2   \        
2*\-1 + tanh (x)/*\2 - 2*tanh (x)/*tanh(x)
$$2 \left(2 - 2 \tanh^{2}{\left(x \right)}\right) \left(\tanh^{2}{\left(x \right)} - 1\right) \tanh{\left(x \right)}$$
Tercera derivada [src]
                  /                   2                                                       \
  /         2   \ |    /         2   \          2            4            2    /         2   \|
2*\-1 + tanh (x)/*\1 + \-1 + tanh (x)/  - 3*tanh (x) + 2*tanh (x) + 7*tanh (x)*\-1 + tanh (x)//
$$2 \left(\tanh^{2}{\left(x \right)} - 1\right) \left(\left(\tanh^{2}{\left(x \right)} - 1\right)^{2} + 7 \left(\tanh^{2}{\left(x \right)} - 1\right) \tanh^{2}{\left(x \right)} + 2 \tanh^{4}{\left(x \right)} - 3 \tanh^{2}{\left(x \right)} + 1\right)$$
Gráfico
Derivada de y=thx-((1/3)th^3x)