## Problem Statement

Find the $n$-th order derivative.

$$
y=\frac{11+12 x}{6 x+5}
$$
## Solution

$y^{\prime}=\left(\frac{11+12 x}{6 x+5}\right)^{\prime}=\frac{12 \cdot(6 x+5)-(11+12 x) \cdot 6}{(6 x+5)^{2}}=$

$=\frac{6 \cdot(12 x+10-11-12 x)}{(6 x+5)^{2}}=-6(6 x+5)^{-2}$

$y^{\prime \prime}=\left(y^{\prime}\right)^{\prime}=\left(-6(6 x+5)^{-2}\right)^{\prime}=$

$=-6 \cdot(-2) \cdot(6 x+5)^{-3} \cdot 6=2 \cdot 6^{2} \cdot(6 x+5)^{-3}$

$y^{\prime \prime \prime}=\left(y^{\prime \prime}\right)^{\prime}=\left(2 \cdot 6^{2} \cdot(6 x+5)^{-3}\right)^{\prime}=$
$=2 \cdot 6^{2} \cdot(-3) \cdot(6 x+5)^{-4} \cdot 6=-2 \cdot 3 \cdot 6^{3} \cdot(-3) \cdot(6 x+5)^{-4}$

Obviously,

$y^{(n)}=(-1)^{n} \cdot n!\cdot 6^{n} \cdot(6 x+5)^{-n-1}$

## Problem Kuznetsov Differentiation $18-24$