Question

Find the derivative of the function. Simplify if possible.

F(x) = arcsin ( square root of sin (11x))

Answer 1

F(x) = arcsin(√ sin(lnx));
F'(x) = (√ sin(lnx))' / √(1-sin(ln(x))) = 1/2(sin(lnx))'sin(lnx)^(-1/2) (1-sin(lnx))^(-1/2) =
= 1/2 cos(lnx) * 1/x* ( sin(lnx)*(1-sin(lnx)) )^(-1/2)