Given that: y = 3x^2 + 6x^1/3 + (2x^3 - 7)/(3x^1/2), x > 0 Find dy/dx, give each term in its simplest form

y = 3x² + 6x^1/3 + (2x³/3 - 7/3)x^-1/2Using the multiplication rule for indices y = 3x² + 6x^1/3 + (2/3)x^5/2 - (7/3)x^-1/2Then differentiate each term with respect to x to find dy/dxdy/dx = 6x + 2x^-2/3 + (10/6)x^3/2 + (7/6)x^-3/2Then simplify each term, as requested in the questiondy/dx = 6x + 2/x^2/3 + (5/3)x^3/2 + 7/6x^3/2