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Derivada de la función/ factorial(x)

Derivada de factorial(x)

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

Ha introducido [src] 
x!
x!x! 
factorial(x)
Primera derivada [src] 
Gamma(1 + x)*polygamma(0, 1 + x)
Γ(x+1)polygamma⁡(0,x+1)\Gamma\left(x + 1\right) \operatorname{polygamma}{\left(0,x + 1 \right)}
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Segunda derivada [src] 
/         2                                \             
\polygamma (0, 1 + x) + polygamma(1, 1 + x)/*Gamma(1 + x)
(polygamma⁡2(0,x+1)+polygamma⁡(1,x+1))Γ(x+1)\left(\operatorname{polygamma}^{2}{\left(0,x + 1 \right)} + \operatorname{polygamma}{\left(1,x + 1 \right)}\right) \Gamma\left(x + 1\right)
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Tercera derivada [src] 
/         3                                                                            \             
\polygamma (0, 1 + x) + 3*polygamma(0, 1 + x)*polygamma(1, 1 + x) + polygamma(2, 1 + x)/*Gamma(1 + x)
(polygamma⁡3(0,x+1)+3polygamma⁡(0,x+1)polygamma⁡(1,x+1)+polygamma⁡(2,x+1))Γ(x+1)\left(\operatorname{polygamma}^{3}{\left(0,x + 1 \right)} + 3 \operatorname{polygamma}{\left(0,x + 1 \right)} \operatorname{polygamma}{\left(1,x + 1 \right)} + \operatorname{polygamma}{\left(2,x + 1 \right)}\right) \Gamma\left(x + 1\right)
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