Question Detail

We are given y = √sin x, which can be written as y = (sin x)1/2.To find the derivative dy/dx, we use the chain rule.The power rule states d/du [un] = n un-1, and with chain rule d/dx [f(g(x))] = f'(g(x)) * g'(x).Here, let u = sin x, so du/dx = cos x.dy/dx = (1/2) (sin x)(1/2)-1 * d/dx(sin x) = (1/2) (sin x)-1/2 * cos x = (1/2) * (1/√sin x) * cos x = cos x / (2√sin x).This matches option B.