Производная factorial(factorial(3*x))

Вы ввели

((3*x)!)!

$$\left(\left(3 x\right)!\right)!$$

Первая производная

3*gamma(1 + 3*x)*gamma(1 + (3*x)!)*polygamma(0, 1 + 3*x)*polygamma(0, 1 + (3*x)!)

$$3 \Gamma{\left(3 x + 1 \right)} \Gamma{\left(\left(3 x\right)! + 1 \right)} \operatorname{polygamma}{\left (0,3 x + 1 \right )} \operatorname{polygamma}{\left (0,\left(3 x\right)! + 1 \right )}$$

Вторая производная

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9*\polygamma (0, 1 + 3*x)*polygamma(0, 1 + (3*x)!) + polygamma(0, 1 + (3*x)!)*polygamma(1, 1 + 3*x) + polygamma (0, 1 + 3*x)*polygamma (0, 1 + (3*x)!)*gamma(1 + 3*x) + polygamma (0, 1 + 3*x)*gamma(1 + 3*x)*polygamma(1, 1 + (3*x)!)/*gamma(1 + 3*x)*gamma(1 + (3*x)!)

$$9 \left(\Gamma{\left(3 x + 1 \right)} \operatorname{polygamma}^{2}{\left (0,3 x + 1 \right )} \operatorname{polygamma}^{2}{\left (0,\left(3 x\right)! + 1 \right )} + \Gamma{\left(3 x + 1 \right)} \operatorname{polygamma}^{2}{\left (0,3 x + 1 \right )} \operatorname{polygamma}{\left (1,\left(3 x\right)! + 1 \right )} + \operatorname{polygamma}^{2}{\left (0,3 x + 1 \right )} \operatorname{polygamma}{\left (0,\left(3 x\right)! + 1 \right )} + \operatorname{polygamma}{\left (0,\left(3 x\right)! + 1 \right )} \operatorname{polygamma}{\left (1,3 x + 1 \right )}\right) \Gamma{\left(3 x + 1 \right)} \Gamma{\left(\left(3 x\right)! + 1 \right)}$$

Третья производная

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27*\polygamma (0, 1 + 3*x)*polygamma(0, 1 + (3*x)!) + polygamma(0, 1 + (3*x)!)*polygamma(2, 1 + 3*x) + gamma (1 + 3*x)*polygamma (0, 1 + 3*x)*polygamma (0, 1 + (3*x)!) + gamma (1 + 3*x)*polygamma (0, 1 + 3*x)*polygamma(2, 1 + (3*x)!) + 3*polygamma (0, 1 + 3*x)*polygamma (0, 1 + (3*x)!)*gamma(1 + 3*x) + 3*polygamma (0, 1 + 3*x)*gamma(1 + 3*x)*polygamma(1, 1 + (3*x)!) + 3*polygamma(0, 1 + 3*x)*polygamma(0, 1 + (3*x)!)*polygamma(1, 1 + 3*x) + 3*gamma (1 + 3*x)*polygamma (0, 1 + 3*x)*polygamma(0, 1 + (3*x)!)*polygamma(1, 1 + (3*x)!) + 3*polygamma (0, 1 + (3*x)!)*gamma(1 + 3*x)*polygamma(0, 1 + 3*x)*polygamma(1, 1 + 3*x) + 3*gamma(1 + 3*x)*polygamma(0, 1 + 3*x)*polygamma(1, 1 + 3*x)*polygamma(1, 1 + (3*x)!)/*gamma(1 + 3*x)*gamma(1 + (3*x)!)

$$27 \left(\Gamma^{2}{\left(3 x + 1 \right)} \operatorname{polygamma}^{3}{\left (0,3 x + 1 \right )} \operatorname{polygamma}^{3}{\left (0,\left(3 x\right)! + 1 \right )} + 3 \Gamma^{2}{\left(3 x + 1 \right)} \operatorname{polygamma}^{3}{\left (0,3 x + 1 \right )} \operatorname{polygamma}{\left (0,\left(3 x\right)! + 1 \right )} \operatorname{polygamma}{\left (1,\left(3 x\right)! + 1 \right )} + \Gamma^{2}{\left(3 x + 1 \right)} \operatorname{polygamma}^{3}{\left (0,3 x + 1 \right )} \operatorname{polygamma}{\left (2,\left(3 x\right)! + 1 \right )} + 3 \Gamma{\left(3 x + 1 \right)} \operatorname{polygamma}^{3}{\left (0,3 x + 1 \right )} \operatorname{polygamma}^{2}{\left (0,\left(3 x\right)! + 1 \right )} + 3 \Gamma{\left(3 x + 1 \right)} \operatorname{polygamma}^{3}{\left (0,3 x + 1 \right )} \operatorname{polygamma}{\left (1,\left(3 x\right)! + 1 \right )} + 3 \Gamma{\left(3 x + 1 \right)} \operatorname{polygamma}{\left (0,3 x + 1 \right )} \operatorname{polygamma}^{2}{\left (0,\left(3 x\right)! + 1 \right )} \operatorname{polygamma}{\left (1,3 x + 1 \right )} + 3 \Gamma{\left(3 x + 1 \right)} \operatorname{polygamma}{\left (0,3 x + 1 \right )} \operatorname{polygamma}{\left (1,3 x + 1 \right )} \operatorname{polygamma}{\left (1,\left(3 x\right)! + 1 \right )} + \operatorname{polygamma}^{3}{\left (0,3 x + 1 \right )} \operatorname{polygamma}{\left (0,\left(3 x\right)! + 1 \right )} + 3 \operatorname{polygamma}{\left (0,3 x + 1 \right )} \operatorname{polygamma}{\left (0,\left(3 x\right)! + 1 \right )} \operatorname{polygamma}{\left (1,3 x + 1 \right )} + \operatorname{polygamma}{\left (0,\left(3 x\right)! + 1 \right )} \operatorname{polygamma}{\left (2,3 x + 1 \right )}\right) \Gamma{\left(3 x + 1 \right)} \Gamma{\left(\left(3 x\right)! + 1 \right)}$$