Знайдіть похідну f(x)=(3х−1)√2х−2 х0=3

[latex]f(x)=(3x-1) \sqrt{2x-2}[/latex] [latex]f'(x)=[(3x-1) \sqrt{2x-2}]'=[/latex] [latex]=(3x-1)'* \sqrt{2x-2}+(3x-1)*( \sqrt{2x-2} )'=[/latex] [latex]=[(3x)'-(1)']* \sqrt{2x-2}+(3x-1)*[(2x-2})^{ \frac{1}{2} }]' =[/latex] [latex]=[3*(x)'-0]* \sqrt{2x-2}+(3x-1)*[\frac{1}{2}*(2x-2})^{ \frac{1}{2}-1 }*(2x-2)']=[/latex] [latex]=[3*1-0]* \sqrt{2x-2}+(3x-1)*\frac{1}{2}*(2x-2})^{ -\frac{1}{2}}*(2x-2)'=[/latex] [latex]=3 \sqrt{2x-2}+(3x-1)* \frac{1}{2}* \frac{1}{(2x-2)^ \frac{1}{2} }}*[(2x)'-(2)']=[/latex] [latex]=3 \sqrt{2x-2}+(3x-1)* \frac{1}{2 \sqrt{2x-2}}}*[2*(x)'-0]=[/latex] [latex]=3 \sqrt{2x-2}+(3x-1)* \frac{1}{2 \sqrt{2x-2}}}*[2*1-0]=[/latex] [latex]=3 \sqrt{2x-2}+(3x-1)* \frac{2*1}{2* \sqrt{2x-2}}}=[/latex] [latex]=3 \sqrt{2x-2}+(3x-1)* \frac{1}{\sqrt{2x-2}}} =3 \sqrt{2x-2}+\frac{3x-1}{\sqrt{2x-2}}}[/latex] [latex]f'(x_0)=f'(3)=3 \sqrt{2*3-2}+\frac{3*3-1}{\sqrt{2*3-2}}}=3 \sqrt{4} + \frac{8}{ \sqrt{4} } =[/latex] [latex]=3*2+ \frac{8}{2}=6+4=10 [/latex] Відповідь: [latex]10[/latex]