## Problem Statement

Find the derivative.

$y=\frac{4+x^{4}}{x^{3}} \cdot \operatorname{arctg} \frac{x^{2}}{2}+\frac{4}{x}$
## Solution

$y^{\prime}=\left(\frac{4+x^{4}}{x^{3}} \cdot \operatorname{arctg} \frac{x^{2}}{2}+\frac{4}{x}\right)^{\prime}=$

$=\frac{4 x^{3} \cdot x^{3}-\left(4+x^{4}\right) \cdot 3 x^{2}}{x^{6}} \cdot \operatorname{arctg} \frac{x^{2}}{2}+\frac{4+x^{4}}{x^{3}} \cdot \frac{1}{1+\left(\frac{x^{2}}{2}\right)^{2}} \cdot x-\frac{4}{x^{2}}=$

$=\frac{4 x^{4}-12-3 x^{4}}{x^{4}} \cdot \operatorname{arctg} \frac{x^{2}}{2}+\frac{4+x^{4}}{x^{3}} \cdot \frac{4}{4+x^{4}} \cdot x-\frac{4}{x^{2}}=$

$=\frac{x^{4}-12}{x^{4}} \cdot \operatorname{arctg} \frac{x^{2}}{2}+\frac{4}{x^{2}}-\frac{4}{x^{2}}=\frac{x^{4}-12}{x^{4}} \cdot \operatorname{arctg} \frac{x^{2}}{2}$

Problem Kuznetsov Differentiation 10-13