## Task Condition

Find the derivative of the specified order.

$$
y=\frac{\log _{2} x}{x^{3}}, y^{\prime \prime \prime}=?
$$
## Solution

$$
\begin{aligned}
& y^{\prime}=\left(\frac{\log _{2} x}{x^{3}}\right)^{\prime}=\left(\frac{\ln x}{\ln 2 \cdot x^{3}}\right)^{\prime}=\frac{\frac{1}{x} \cdot x^{3}-\ln x \cdot 3 x^{2}}{\ln 2 \cdot x^{6}}= \\
& =\frac{1-3 \ln x}{\ln 2 \cdot x^{4}} \\
& y^{\prime \prime}=\left(y^{\prime}\right)^{\prime}=\left(\frac{1-3 \ln x}{\ln 2 \cdot x^{4}}\right)^{\prime}=\frac{-3 \cdot \frac{1}{x} \cdot x^{4}-(1-3 \ln x) \cdot 4 x^{3}}{\ln 2 \cdot x^{8}}= \\
& =\frac{-3-4(1-3 \ln x)}{\ln 2 \cdot x^{5}}=\frac{-7+12 \ln x}{\ln 2 \cdot x^{5}} \\
& y^{\prime \prime \prime}=\left(y^{\prime \prime}\right)^{\prime}=\left(\frac{-7+12 \ln x}{\ln 2 \cdot x^{5}}\right)^{\prime}=\frac{12 \cdot \frac{1}{x} \cdot x^{5}-(-7+12 \ln x) \cdot 5 x^{4}}{\ln 2 \cdot x^{10}}= \\
& =\frac{12-5(-7+12 \ln x)}{\ln 2 \cdot x^{6}}=\frac{47-60 \ln x}{\ln 2 \cdot x^{6}}
\end{aligned}
$$

## Problem Kuznetsov Differentiation 19-5