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 + 6x1/3 + (2x3/3 - 7/3)x-1/2Using the multiplication rule for indices y = 3x2 + 6x1/3 + (2/3)x5/2 - (7/3)x-1/2Then differentiate each term with respect to x to find dy/dxdy/dx = 6x + 2x-2/3 + (10/6)x3/2 + (7/6)x-3/2Then simplify each term, as requested in the questiondy/dx = 6x + 2/x2/3 + (5/3)x3/2 + 7/6x3/2
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