13. Find the derivative of the following function by first expanding the expression. \[ f(x)=(2 x+3)\left(3 x^{2}+1\right) \] \( f^{\prime}(x)=\square \)

Исследовать на сходимость ряды с положительными членами \( \sum_{n=1}^{\infty} \frac{(n+2)!}{n^{n}} \). \( \sum_{n=1}^{\infty} \frac{n+3}{n(n+1)} \)

11. Sia data la funzione \( f \), derivabile in \( \mathbb{R} \), tale che \( f(0)=-5, f^{\prime}(0)=-4 \). Allora \( g(x)=|f(x)| \) a) \( g(x) \) presenta un punto angoloso in \( x=0 \) b) \( P(0,5) \in g(x) \) e \( g^{\prime}(0)=-4 \) c) \( g \) è derivabile in \( x=0 \) e \( g^{\prime}(0)=4 \) d) \( g \) è derivabile in \( x=0 \) e \( g^{\prime}(0)=-4 \) e) \( \lim _{x \rightarrow 0^{-}} g^{\prime}(x)=-4 ; \lim _{x \rightarrow 0^{+}} g^{\prime}(x)=4 \)

Find \( \frac{d^{2} y}{d x^{2}} \) given \( x^{3}-3 x y+y^{3}=1 \)

1. The integral \( \int_{\pi / 6}^{\pi / 3} \tan ^{3} x \cdot \sin ^{2} 3 x\left(2 \sec ^{2} x \cdot \sin ^{2} 3 x+3 \tan x \cdot \sin 6 x\right) d x \) \( \begin{array}{ll}\text { (1) } \frac{9}{2} & \text { (2) }-\frac{1}{9} \\ \text { (3) } \frac{7}{18} & \text { (4) }-\frac{1}{18}\end{array} \)

\( \operatorname { m } _ { \rightarrow 0 } ( \frac { ( \sin ( x ) ^ { 2 } \times \cos ( \frac { 1 } { x } ) ) } { x } ) \)