Find f '(0.4) for f of x equals the integral from 0 to x of the arcsine of t, dt

Question

Find f '(0.4) for 

0.081 

0.412 

0.389 

1.091

Answer 1

f(x) = ∫_{(from 0 to x)} Arcsint dt

Using the Fundamental Theorem, f'(x) = Arcsinx

So, f'(0.4) = Arcsin(0.4) ≈ 0.412