## Task Condition

Find the derivative.

$y=\log _{16} \log _{5} \operatorname{tg} x$
## Solution

$y^{\prime}=\left(\log _{16} \log _{5} \operatorname{tg} x\right)^{\prime}=\frac{1}{\log _{5} \operatorname{tg} x \cdot \ln 16} \cdot\left(\log _{5} \operatorname{tg} x\right)^{\prime}=$

$=\frac{1}{\log _{5} \operatorname{tg} x \cdot \ln 16} \cdot \frac{1}{\operatorname{tg} x \cdot \ln 5} \cdot \frac{1}{\cos ^{2} x}=$

$=\frac{1}{2 \sin x \cdot \cos x \cdot \ln 4 \cdot \ln 5 \cdot \log _{5} \operatorname{tg} x}=$

$=\frac{1}{\sin 2 x \cdot \ln 4 \cdot \ln 5 \cdot \frac{\operatorname{lntg} x}{\ln 5}}=\frac{1}{\sin 2 x \cdot \ln 4 \cdot \ln \operatorname{tg} x}$

## Problem Kuznetsov Differentiation 8-14