Найти производную n-го порядка

Задача 1. Найти производную \(n\)-го порядка.
\[y = {a^{3x}}.\]
Решение.
\[\begin{array}{l}y' = 3{a^{3x}}\ln a,\\y'' = 9{a^{3x}}{\ln ^2}a,\\{y^{(n)}} = {3^n}{a^{3x}}{(\ln a)^{(n)}}.\end{array}\]

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Решение.\[\begin{array}{l}y' = 4x\ln (x - 1) + \frac{{2{x^2} - 7}}{{x - 1}},\\y'' = 4\ln (x - 1) + \frac{{4x}}{{x - 1}} + \frac{{4x(x - 1) - (2{x^2} - 7)}}{{{{(x - 1)}^2}}} = \\ = 4\ln (x - 1) + \frac{{4x}}{{x - 1}} + \frac{{2{x^2} - 4x + 7}}{{{{(x - 1)}^2}}},\\y''' = \frac{4}{{x - 1}} + \frac{{4(x - 1) - 4x}}{{{{(x - 1)}^2}}} + \\ + \frac{{(4x - 4){{(x - 1)}^2} - 2(x - 1)(2{x^2} - 4x + 7)}}{{{{(x - 1)}^4}}} = \\ = \frac{4}{{x - 1}} - \frac{4}{{{{(x - 1)}^2}}} - \frac{{10}}{{{{(x - 1)}^3}}},\\{y^{|V}} =  - \frac{4}{{{{(x - 1)}^2}}} + \frac{8}{{{{(x - 1)}^3}}} + \frac{{30}}{{{{(x - 1)}^4}}},\\{y^V} = \frac{8}{{{{(x - 1)}^3}}} - \frac{{24}}{{{{(x - 1)}^4}}} - \frac{{120}}{{{{(x - 1)}^5}}}.\end{array}\]