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x*tanh(ln(1+exp(x)))
Derivada de la función/ exp(x)/ x*tanh(ln(1+exp(x)))

Derivada de x*tanh(ln(1+exp(x)))

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

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Solución

Ha introducido [src] 
      /   /     x\\
x*tanh\log\1 + e //
xtanh⁡(log⁡(ex+1))x \tanh{\left(\log{\left(e^{x} + 1 \right)} \right)} 
x*tanh(log(1 + exp(x)))
Gráfica
02468-8-6-4-2-101020-10
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Trazar el gráfico f'(x)
Primera derivada [src] 
  /        2/   /     x\\\  x                    
x*\1 - tanh \log\1 + e ///*e        /   /     x\\
----------------------------- + tanh\log\1 + e //
                 x                               
            1 + e
x(1−tanh⁡2(log⁡(ex+1)))exex+1+tanh⁡(log⁡(ex+1))\frac{x \left(1 - \tanh^{2}{\left(\log{\left(e^{x} + 1 \right)} \right)}\right) e^{x}}{e^{x} + 1} + \tanh{\left(\log{\left(e^{x} + 1 \right)} \right)}
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Segunda derivada [src] 
                          /       /        x        x     /   /     x\\\\   
/         2/   /     x\\\ |       |       e      2*e *tanh\log\1 + e //||  x
\-1 + tanh \log\1 + e ///*|-2 + x*|-1 + ------ + ----------------------||*e 
                          |       |          x                x        ||   
                          \       \     1 + e            1 + e         //   
----------------------------------------------------------------------------
                                        x                                   
                                   1 + e
(x(−1+2extanh⁡(log⁡(ex+1))ex+1+exex+1)−2)(tanh⁡2(log⁡(ex+1))−1)exex+1\frac{\left(x \left(-1 + \frac{2 e^{x} \tanh{\left(\log{\left(e^{x} + 1 \right)} \right)}}{e^{x} + 1} + \frac{e^{x}}{e^{x} + 1}\right) - 2\right) \left(\tanh^{2}{\left(\log{\left(e^{x} + 1 \right)} \right)} - 1\right) e^{x}}{e^{x} + 1}
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Tercera derivada [src] 
                          /       /        x         2*x       x     /   /     x\\     /         2/   /     x\\\  2*x         2/   /     x\\  2*x      2*x     /   /     x\\\       x       x     /   /     x\\\   
/         2/   /     x\\\ |       |     3*e       2*e       6*e *tanh\log\1 + e //   2*\-1 + tanh \log\1 + e ///*e      4*tanh \log\1 + e //*e      6*e   *tanh\log\1 + e //|    3*e     6*e *tanh\log\1 + e //|  x
\-1 + tanh \log\1 + e ///*|-3 - x*|1 - ------ + --------- - ---------------------- + -------------------------------- + ------------------------- + ------------------------| + ------ + ----------------------|*e 
                          |       |         x           2                x                              2                               2                          2        |        x                x        |   
                          |       |    1 + e    /     x\            1 + e                       /     x\                        /     x\                   /     x\         |   1 + e            1 + e         |   
                          \       \             \1 + e /                                        \1 + e /                        \1 + e /                   \1 + e /         /                                  /   
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                            x                                                                                                      
                                                                                                       1 + e
(tanh⁡2(log⁡(ex+1))−1)(−x(1−6extanh⁡(log⁡(ex+1))ex+1−3exex+1+2(tanh⁡2(log⁡(ex+1))−1)e2x(ex+1)2+4e2xtanh⁡2(log⁡(ex+1))(ex+1)2+6e2xtanh⁡(log⁡(ex+1))(ex+1)2+2e2x(ex+1)2)−3+6extanh⁡(log⁡(ex+1))ex+1+3exex+1)exex+1\frac{\left(\tanh^{2}{\left(\log{\left(e^{x} + 1 \right)} \right)} - 1\right) \left(- x \left(1 - \frac{6 e^{x} \tanh{\left(\log{\left(e^{x} + 1 \right)} \right)}}{e^{x} + 1} - \frac{3 e^{x}}{e^{x} + 1} + \frac{2 \left(\tanh^{2}{\left(\log{\left(e^{x} + 1 \right)} \right)} - 1\right) e^{2 x}}{\left(e^{x} + 1\right)^{2}} + \frac{4 e^{2 x} \tanh^{2}{\left(\log{\left(e^{x} + 1 \right)} \right)}}{\left(e^{x} + 1\right)^{2}} + \frac{6 e^{2 x} \tanh{\left(\log{\left(e^{x} + 1 \right)} \right)}}{\left(e^{x} + 1\right)^{2}} + \frac{2 e^{2 x}}{\left(e^{x} + 1\right)^{2}}\right) - 3 + \frac{6 e^{x} \tanh{\left(\log{\left(e^{x} + 1 \right)} \right)}}{e^{x} + 1} + \frac{3 e^{x}}{e^{x} + 1}\right) e^{x}}{e^{x} + 1}
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Gráfico
Derivada de x*tanh(ln(1+exp(x)))
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