357. Find \( f^{\prime}(1 / 5) \) if \( f(x)=\operatorname{arctg} 5 x+x^{2} \).
Solution. We have

$$
f^{\prime}(x)=\frac{1}{1+(5 x)^{2}} \cdot(5 x)^{\prime}+2 x=\frac{5}{1+25 x^{2}}+2 x
$$

Therefore,

$$
f^{\prime}(1 / 5)=\frac{5}{1+25 \cdot \frac{1}{25}}+2 \cdot \frac{1}{5}=\frac{5}{2}+\frac{2}{5}=2.5+0.4=2.9
$$