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d/dx arcsin(sqrt(x)) =

A1/(2 sqrt(x) × sqrt(1-x)) (chain rule)
Bln(x)
C1/sqrt(1-x)
D1/sqrt(x(1-x))
Answer & Solution
Correct answer: A. 1/(2 sqrt(x) × sqrt(1-x)) (chain rule)
d/dx arcsin(u) = (1/sqrt(1-u²)) du/dx with u = sqrt(x). du/dx = 1/(2 sqrt(x)). 1 - u² = 1 - x. **So derivative = 1/[2 sqrt(x) sqrt(1-x)].**
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