Обычное правило.
R-расстояние
S-скорость
V-время
R=S*V, S=R:V, V=R:S
1)30
2)15
3)6
4)5
вот и все )
A) y=4x*e^2x
y' = 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^2x
Б) 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))
А) (6 см 4 мм + 8 см) * 2 = 14 см 4 мм * 2 = 14,4 * 2 = 28,8 см = 28 см 8 мм
б) (5 дм + 2 м) * 2 = (5 дм + 20 дм) * 2 = 25 * 2 = 50 дм = 5 м