## Task Condition

Find the derivative of the specified order.

$y=\frac{\ln x}{x^{5}}, y^{\prime \prime \prime}=?$
## Solution

$y^{\prime}=\left(\frac{\ln x}{x^{5}}\right)^{\prime}=\frac{\frac{1}{x} \cdot x^{5}-\ln x \cdot 5 x^{4}}{x^{10}}=\frac{1-5 \ln x}{x^{6}}$

$y^{\prime \prime}=\left(y^{\prime}\right)^{\prime}=\left(\frac{1-5 \ln x}{x^{6}}\right)^{\prime}=\frac{-5 \cdot \frac{1}{x} \cdot x^{6}-(1-5 \ln x) \cdot 6 x^{5}}{x^{12}}=$

$=\frac{-5-6(1-5 \ln x)}{x^{7}}=\frac{-11+30 \ln x}{x^{7}}$

$y^{\prime \prime \prime}=\left(y^{\prime \prime}\right)^{\prime}=\left(\frac{-11+30 \ln x}{x^{7}}\right)^{\prime}=\frac{30 \cdot \frac{1}{x} \cdot x^{7}-(-11+30 \ln x) \cdot 7 x^{6}}{x^{14}}=$

$=\frac{30-7(-11+30 \ln x)}{x^{8}}=\frac{107-210 \ln x}{x^{8}}$

Problem Kuznetsov Differentiation 19-23