find the derivative of :(x^2+5x-3)/(3x^1/2)

Answer 1

just doing the division, you have
1/3 (x^(3/2) + 5x^(1/2) - 3x^(-1/2))
so just apply the power rule to get
1/3 (3x^(1/2) + 5/2 x^(-1/2) + 3/2 x^(-3/2))

The quotient rule gives the same result, as
((2x+5)(3x^(1/2) + (x^2 + 5x - 3)(3/2 x^(-1/2)) / 9x