[tex]f'(x)=\left(x-5\right)'\cdot \left({x}^{2}+3\right)+\left({x}^{2}+3\right)'\cdot \left(x-5\right)=\left(\left(x\right)'-\left(5\right)'\right)\cdot \left({x}^{2}+3\right)+\left(\left({x}^{2}\right)'+\left(3\right)'\right)\cdot \left(x-5\right)=\\=\left(1-0\right)\cdot \left({x}^{2}+3\right)+\left(2\cdot x+0\right)\cdot \left(x-5\right)={x}^{2}+2\,\left(x-5\right)\,x+3[/tex]

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