Resposta:
Explicação passo-a-passo:
1)
[tex]j(x) = \frac{x - 1}{x + 1} \\j'(x) = \frac{1 . (x + 1) - 1 (x - 1)}{(x + 1)^{2} } \\j'(x) = \frac{x + 1 - x + 1}{(x + 1)^{2}} \\\\j'(x) = \frac{2}{(x + 1)^{2} } \\\\[/tex]
2)
[tex]y = x \sqrt{2x - x^{2} } \\y = x . (2x - x^{2} )^{\frac{1}{2} } \\y' = 1 . \sqrt{2x - x^{2} } + \frac{(1 - x) . x }{\sqrt{2x - x^{2} } }\\y' = \sqrt{2x - x^{2} } . \frac{\sqrt{2x - x^{2} } }{\sqrt{2x - x^{2} } } + \frac{(1 - x) . x }{\sqrt{2x - x^{2} } }\\y' = \frac{{2x - x^{2} } }{\sqrt{2x - x^{2} } } + \frac{x - x^{2}) }{\sqrt{2x - x^{2} } }\\y' = \frac{3x - 2x^{2} }{\sqrt{2x - x^{2} } }[/tex]
