The answer is -6x^-5/2 but I don't know how to get it!
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g(x) = (x^2 + 4x^(1/2))/x^2 = distributive law
= x^2/x^2 + 4x^(1/2)/x^2 =
= 1 + 4 x^(1/2 - 2) =
= 1 + 4x^(-3/2)
g'(x) = 4·(-3/2) x^(-3/2 - 1)
g'(x) = - 6x^(-5/2) = - 6/(x²√x)
= x^2/x^2 + 4x^(1/2)/x^2 =
= 1 + 4 x^(1/2 - 2) =
= 1 + 4x^(-3/2)
g'(x) = 4·(-3/2) x^(-3/2 - 1)
g'(x) = - 6x^(-5/2) = - 6/(x²√x)
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just plug it into www.wolframalpha.com