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We consider a new Sobolev type function space called the space with multiweighted derivatives $W_{p,\overline{\alpha }}^n$, where $\overline{\alpha }=({\alpha }_0,{\alpha }_1,...,{\alpha }_n)$, ${\alpha }_i\in ℝ$, $i=0,1,...,n$, and ${\parallel f\parallel }_{W_{p,\overline{\alpha }}^n}=\parallel D_{\overline{\alpha }}^n{f\parallel }_p+{\sum }_{i=0}^{n-1}\left|D_{\overline{\alpha }}^{i}f\left(1\right)\right|$, $$D_{\overline{\alpha }}^{0}f\left(t\right)=t^{{\alpha }_0}f\left(t\right),D_{\overline{\alpha }}^{i}f\left(t\right)=t^{{\alpha }_i}\frac{\mathrm{d}}{\mathrm{d}t}{D}_{\overline{\alpha }}^{i-1}f\left(t\right),i=1,2,...,n.$$ We establish necessary and sufficient conditions for the boundedness and compactness of the embedding $W_{p,\overline{\alpha }}^n\hookrightarrow W_{q,\overline{\beta }}^m$, when $1\le q<p<\infty$, $0\le m<n$.