[tex]y =\frac{v^3 - 2v\sqrt{v}}{v}=\frac{v^3 - 2v^{\frac{3}{2}}}{v}
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\\y ='(\frac{v^3 - 2v^{\frac{3}{2}}}{v})'= \frac{(v^3 - 2v^{\frac{3}{2}})'v-(v^3 - 2v^{\frac{3}{2}})v^' }{v^2} = \frac{(3v^2-3 \sqrt{v})v-(v^3 - 2v \sqrt{v} ) }{v^2} =
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\\=\frac{(3v^2-3 \sqrt{v})v-v(v^2 - 2 \sqrt{v} ) }{v^2} =\frac{v(3v^2-3 \sqrt{v}-v^2 +2 \sqrt{v} ) }{v^2} =\frac{2v^2- \sqrt{v} }{v} =\frac{2v\sqrt{v}-1 }{ \sqrt{v} } [/tex]
