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y=ln(coshx)+1/2cosh^2x
Derivada de la función/ coshx/ y=ln(coshx)+1/2cosh^2x

Derivada de y=ln(coshx)+1/2cosh^2x

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

Ha introducido [src] 
                   2   
               cosh (x)
log(cosh(x)) + --------
                  2
log⁡(cosh⁡(x))+cosh⁡2(x)2\log{\left(\cosh{\left(x \right)} \right)} + \frac{\cosh^{2}{\left(x \right)}}{2} 
log(cosh(x)) + cosh(x)^2/2
Gráfica
02468-8-6-4-2-1010-200000000200000000
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
sinh(x)                  
------- + cosh(x)*sinh(x)
cosh(x)
sinh⁡(x)cosh⁡(x)+sinh⁡(x)cosh⁡(x)\sinh{\left(x \right)} \cosh{\left(x \right)} + \frac{\sinh{\left(x \right)}}{\cosh{\left(x \right)}}
Simplificar
Segunda derivada [src] 
                              2   
        2          2      sinh (x)
1 + cosh (x) + sinh (x) - --------
                              2   
                          cosh (x)
sinh⁡2(x)−sinh⁡2(x)cosh⁡2(x)+cosh⁡2(x)+1\sinh^{2}{\left(x \right)} - \frac{\sinh^{2}{\left(x \right)}}{\cosh^{2}{\left(x \right)}} + \cosh^{2}{\left(x \right)} + 1
Simplificar
Tercera derivada [src] 
  /                            2   \        
  |     1                  sinh (x)|        
2*|- ------- + 2*cosh(x) + --------|*sinh(x)
  |  cosh(x)                   3   |        
  \                        cosh (x)/
2(sinh⁡2(x)cosh⁡3(x)+2cosh⁡(x)−1cosh⁡(x))sinh⁡(x)2 \left(\frac{\sinh^{2}{\left(x \right)}}{\cosh^{3}{\left(x \right)}} + 2 \cosh{\left(x \right)} - \frac{1}{\cosh{\left(x \right)}}\right) \sinh{\left(x \right)}
Simplificar
Gráfico
Derivada de y=ln(coshx)+1/2cosh^2x
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