Sr Examen

Derivada de x!

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

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Solución

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