Найти производные:
A) y=4x*e^2x

Б) y=ln tg^2 x/6

A) y=4x*e^2xy' = 4*(x*e^2x)' = 4*( x' * e^2x + x*(e^2x)' ) =4*( 1 * e^2x + x*(e^2x)*(2x)' ) =4*( e^2x + x*(e^2x)*2 ) = 4 * e^2x + x*(e^2x)*8 =4 * e^2x + 8 * x * e^2xБ) y=ln (tg^2 (x/6))y' = 1/tg^2 (x/6) * (tg^2 (x/6))' = 1/tg^2 (x/6) * 2*(tg^(2-1) (x/6)) * (tg (x/6))' =1/tg^2 (x/6) * 2*(tg^1 (x/6)) * (tg (x/6))' =1/tg^2 (x/6) * 2*(tg (x/6)) * (1/cos^2 (x/6)) * (x/6)' =1/tg (x/6) * 2 * (1/cos^2 (x/6)) * (x/6)' =1/tg (x/6) * 2 * (1/(cos^2 (x/6)) ) * (1/6) =(2/6) * 1/tg (x/6) * (1/(cos^2 (x/6)) )=(1/3) * 1/tg (x/6) * (1/(cos^2 (x/6)) )=(1/3) * (cos (x/6)/sin (x/6)) * (1/(cos^2 (x/6)) )=(1/3) * (1/sin (x/6)) * (1/(cos (x/6)) )=(1/3) * (1/( (sin (x/6)) * (cos (x/6)) ) )=(1/3) * ( 1/( (1/2)*sin(2x/6) ) ) = (1/3) * (2/(sin(2x/6) ) ) =(1/3) * (2/(sin(x/3) ) ) =(2/3) * (1/(sin(x/3) ) ) =2 / (3*sin(x/3))