Question Detail

To find the derivative of √(7-2x³), first rewrite it as (7-2x³)¹/₂. Then, apply the chain rule: d/dx [u&supn;] = n u&sup(n-1) * du/dx.Let u = 7-2x³ and n = 1/2.First, find du/dx: d/dx (7-2x³) = -6x².Now, apply the chain rule:dy/dx = (1/2) * (7-2x³)&sup(1/2 - 1) * (-6x²).dy/dx = (1/2) * (7-2x³)&sup(−1/₂) * (-6x²).dy/dx = -3x² / (7-2x³)¹/₂ = -3x² / √(7-2x³).Option B matches this result.