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y=x^2lnsinhx
Derivada de la función/ sinhx/ y=x^2/ y=x^2lnsinhx

Derivada de y=x^2lnsinhx

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

Ha introducido [src] 
 2             
x *log(sinh(x))
x2log⁡(sinh⁡(x))x^{2} \log{\left(\sinh{\left(x \right)} \right)} 
x^2*log(sinh(x))
Gráfica
02468-8-6-4-2-1010-10001000
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Trazar el gráfico f'(x)
Primera derivada [src] 
                    2        
                   x *cosh(x)
2*x*log(sinh(x)) + ----------
                    sinh(x)
x2cosh⁡(x)sinh⁡(x)+2xlog⁡(sinh⁡(x))\frac{x^{2} \cosh{\left(x \right)}}{\sinh{\left(x \right)}} + 2 x \log{\left(\sinh{\left(x \right)} \right)}
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Segunda derivada [src] 
                    /        2   \              
                  2 |    cosh (x)|   4*x*cosh(x)
2*log(sinh(x)) + x *|1 - --------| + -----------
                    |        2   |     sinh(x)  
                    \    sinh (x)/
x2(1−cosh⁡2(x)sinh⁡2(x))+4xcosh⁡(x)sinh⁡(x)+2log⁡(sinh⁡(x))x^{2} \left(1 - \frac{\cosh^{2}{\left(x \right)}}{\sinh^{2}{\left(x \right)}}\right) + \frac{4 x \cosh{\left(x \right)}}{\sinh{\left(x \right)}} + 2 \log{\left(\sinh{\left(x \right)} \right)}
Simplificar
Tercera derivada [src] 
  /                                    /        2   \        \
  |                                  2 |    cosh (x)|        |
  |                                 x *|1 - --------|*cosh(x)|
  |    /        2   \                  |        2   |        |
  |    |    cosh (x)|   3*cosh(x)      \    sinh (x)/        |
2*|3*x*|1 - --------| + --------- - -------------------------|
  |    |        2   |    sinh(x)             sinh(x)         |
  \    \    sinh (x)/                                        /
2(−x2(1−cosh⁡2(x)sinh⁡2(x))cosh⁡(x)sinh⁡(x)+3x(1−cosh⁡2(x)sinh⁡2(x))+3cosh⁡(x)sinh⁡(x))2 \left(- \frac{x^{2} \left(1 - \frac{\cosh^{2}{\left(x \right)}}{\sinh^{2}{\left(x \right)}}\right) \cosh{\left(x \right)}}{\sinh{\left(x \right)}} + 3 x \left(1 - \frac{\cosh^{2}{\left(x \right)}}{\sinh^{2}{\left(x \right)}}\right) + \frac{3 \cosh{\left(x \right)}}{\sinh{\left(x \right)}}\right)
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Gráfico
Derivada de y=x^2lnsinhx
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