## Task Condition

Find the derivative of the specified order.

$y=\frac{\ln x}{x^{2}}, y^{IV}=?$
## Solution

$y^{\prime}=\left(\frac{\ln x}{x^{2}}\right)^{\prime}=\frac{\frac{1}{x} \cdot x^{2}-\ln x \cdot 2 x}{x^{4}}=\frac{1-2 \ln x}{x^{3}}$
$y^{\prime \prime}=\left(y^{\prime}\right)^{\prime}=\left(\frac{1-2 \ln x}{x^{3}}\right)^{\prime}=\frac{\frac{-2}{x} \cdot x^{3}-(1-2 \ln x) 3 x^{2}}{x^{6}}=$

$=\frac{-2-3(1-2 \ln x)}{x^{4}}=\frac{-5+6 \ln x}{x^{4}}$

$y^{\prime \prime \prime}=\left(y^{\prime \prime}\right)^{\prime}=\left(\frac{-5+6 \ln x}{x^{4}}\right)^{\prime}=\frac{\frac{6}{x} \cdot x^{4}-(-5+6 \ln x) \cdot 4 x^{3}}{x^{8}}=$

$=\frac{6-4(-5+6 \ln x)}{x^{5}}=\frac{26-24 \ln x}{x^{5}}$

$y^{(I V)}=\left(y^{\prime \prime \prime}\right)^{\prime}=\left(\frac{26-24 \ln x}{x^{5}}\right)^{\prime}=\frac{\frac{-24}{x} \cdot x^{5}-(26-24 \ln x) \cdot 5 x^{4}}{x^{10}}=$

$=\frac{-154+120 \ln x}{x^{6}}$

## Problem Kuznetsov Differentiation 19-8