Question #1701

Find the derivative of the function. Simplify if possible.
F(x) = arcsin ( square root of sin (11x))

Expert's answer

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)}

F'(x) = (√ sin(lnx))' / √(1-sin(ln(x))) = 1/2(sin(lnx))'sin(lnx)

= 1/2 cos(lnx) * 1/x* ( sin(lnx)*(1-sin(lnx)) )

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