Найти производную функции y=ln^2*(arcsin(2x-4))

Question

Найти производную функции y=ln^2*(arcsin(2x-4))

Answer 1

y=ln^2*(arcsin(2x-4))
y'=2*ln(arcsin(2x-4))*(ln(arcsin(2x-4)))'=
= (2ln(arcsin(2x-4))/arcsin(2x-4))*(arcsin(2x-4))'=
=(2ln(arcsin(2x-4))/(arcsin(2x-4)*sqrt(1-(2x-4)^2)))*(2x-4)' =
= 4ln(arcsin(2x-4))/(arcsin(2x-4)*sqrt(1-(2x-4)^2))

sqrt - квадратный корень