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\begin{align*}\begin{aligned}&\frac{\mathrm{d}}{\mathbf{d x}} \ln \left(3+\mathrm{e}^{2 \mathrm{x}}\right)=\frac{1}{3+\mathrm{e}^{2 \mathrm{x}}} \mathbf{D}\left(3+\mathrm{e}^{2 \mathrm{x}}\right)=\frac{2 \mathrm{e}^{2 \mathrm{x}}}{3+\mathrm{e}^{2 \mathrm{x}}} \\&\mathbf{D}(\arcsin (1+3 \mathrm{x}))=\frac{1}{\sqrt{1-(1+3 \mathrm{x})^{2}}} \mathbf{D}(1+3 \mathrm{x})=\frac{\mathbf{3}}{\sqrt{1-(1+3 \mathrm{x})^{2}}}\end{aligned}\end{align*}