358. Given: $f(x)=\operatorname{arcctg} \frac{x}{2}-\operatorname{arctg} \sqrt{x}$. Find $f^{\prime}(1)$.
Solution. $f^{\prime}(x)=-\frac{1}{1+\left(\frac{x}{2}\right)^{2}} \cdot\left(\frac{x}{2}\right)^{\prime}-\frac{1}{1+(\sqrt{x})^{2}} \cdot(\sqrt{x})^{\prime}=$

$$
\begin{aligned}
& =-\frac{\frac{1}{2}}{1+\frac{x^{2}}{4}}-\frac{1}{1+x} \cdot \frac{1}{2 \sqrt{x}}=-\frac{1}{2\left(1+\frac{x^{2}}{4}\right)}-\frac{1}{2(1+x) \sqrt{x}} \\
& f^{\prime}(1)=-\frac{1}{2\left(1+\frac{1}{4}\right)}-\frac{1}{2(1+1)}=-\frac{2}{5}-\frac{1}{4}=-\frac{13}{20}
\end{aligned}
$$

359-372. Find the derivatives of the following functions: