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y=th√x/x+1
Derivada de la función/ x/x+1/ y=th√x/x+1

Derivada de y=th√x/x+1

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

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src] 
    /  ___\    
tanh\\/ x /    
----------- + 1
     x
1+tanh⁡(x)x1 + \frac{\tanh{\left(\sqrt{x} \right)}}{x} 
tanh(sqrt(x))/x + 1
Gráfica
02468-8-6-4-2-1010-2020
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Trazar el gráfico f'(x)
Primera derivada [src] 
        2/  ___\       /  ___\
1 - tanh \\/ x /   tanh\\/ x /
---------------- - -----------
        3/2              2    
     2*x                x
−tanh⁡(x)x2+1−tanh⁡2(x)2x32- \frac{\tanh{\left(\sqrt{x} \right)}}{x^{2}} + \frac{1 - \tanh^{2}{\left(\sqrt{x} \right)}}{2 x^{\frac{3}{2}}}
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Segunda derivada [src] 
      /  ___\     /         2/  ___\\   /         2/  ___\\     /  ___\
2*tanh\\/ x /   5*\-1 + tanh \\/ x //   \-1 + tanh \\/ x //*tanh\\/ x /
------------- + --------------------- + -------------------------------
       3                   5/2                           2             
      x                 4*x                           2*x
(tanh⁡2(x)−1)tanh⁡(x)2x2+2tanh⁡(x)x3+5(tanh⁡2(x)−1)4x52\frac{\left(\tanh^{2}{\left(\sqrt{x} \right)} - 1\right) \tanh{\left(\sqrt{x} \right)}}{2 x^{2}} + \frac{2 \tanh{\left(\sqrt{x} \right)}}{x^{3}} + \frac{5 \left(\tanh^{2}{\left(\sqrt{x} \right)} - 1\right)}{4 x^{\frac{5}{2}}}
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Tercera derivada [src] 
 /                                   2                                                                                                \
 |      /  ___\   /         2/  ___\\       /         2/  ___\\       2/  ___\ /         2/  ___\\     /         2/  ___\\     /  ___\|
 |6*tanh\\/ x /   \-1 + tanh \\/ x //    33*\-1 + tanh \\/ x //   tanh \\/ x /*\-1 + tanh \\/ x //   9*\-1 + tanh \\/ x //*tanh\\/ x /|
-|------------- + -------------------- + ---------------------- + -------------------------------- + ---------------------------------|
 |       4                  5/2                     7/2                           5/2                                  3              |
 \      x                4*x                     8*x                           2*x                                  4*x               /
−(9(tanh⁡2(x)−1)tanh⁡(x)4x3+6tanh⁡(x)x4+(tanh⁡2(x)−1)24x52+(tanh⁡2(x)−1)tanh⁡2(x)2x52+33(tanh⁡2(x)−1)8x72)- (\frac{9 \left(\tanh^{2}{\left(\sqrt{x} \right)} - 1\right) \tanh{\left(\sqrt{x} \right)}}{4 x^{3}} + \frac{6 \tanh{\left(\sqrt{x} \right)}}{x^{4}} + \frac{\left(\tanh^{2}{\left(\sqrt{x} \right)} - 1\right)^{2}}{4 x^{\frac{5}{2}}} + \frac{\left(\tanh^{2}{\left(\sqrt{x} \right)} - 1\right) \tanh^{2}{\left(\sqrt{x} \right)}}{2 x^{\frac{5}{2}}} + \frac{33 \left(\tanh^{2}{\left(\sqrt{x} \right)} - 1\right)}{8 x^{\frac{7}{2}}})
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Gráfico
Derivada de y=th√x/x+1
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