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= x^-1 + x^3 - √2 x^(1/2)
g'(x) = -x^(-1-1) + 3 x^(3-1) - √2 (1/2 x^(1/2-1)
= -1/(x^2) + 3 x^2 - 1/2 √2 (1/√x)