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Мастер-Эксперт
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04.02.2010, 05:28
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это ответ
Здравствуйте, Сласти.
1. y’ = ((9 + 6x3/5)1/11)’ = 1/11 ∙ (9 + 6x3/5)1/11 – 1 ∙ (9 + 6x3/5)’ = 1/11 ∙ (9 + 6x3/5)-10/11 ∙ 6 ∙ 3/5 ∙ x3/5 – 1 =
= 18/55 ∙ x-2/5 ∙ (9 + 6x3/5)-10/11.
2. y’ = (lg (x – cos x))’ = 1/ln 10 ∙ (ln (x – cos x))’ = 1/ln 10 ∙ 1/(x – cos x) ∙ (x – cos x)’ = 1/ln 10 ∙ 1/(x – cos x) ∙ (1 + sin x).
3. y’ = (cos ((arcsin x)/2))’ = -sin ((arcsin x)/2) ∙ ((arcsin x)/2)’ = -1/2 ∙ sin ((arcsin x)/2) ∙ (1 – x2)-1/2.
4. y = (x + 1)1/(x + 1), ln y = 1/(x + 1) ∙ ln (x + 1), (ln y)’ = (1/(x + 1) ∙ ln (x + 1))’,
y'/y = (1/(x + 1))’ ∙ ln (x + 1) + 1/(x + 1) ∙ (ln (x + 1))’ = -1/(x + 1)2 ∙ ln (x + 1) + 1/(x + 1) ∙ 1/(x + 1) =
= 1/(x + 1)2 ∙ (1 – ln (x + 1)),
y' = y ∙ 1/(x + 1)2 ∙ (1 – ln (x + 1)) = (x + 1)1/(x + 1) ∙ 1/(x + 1)2 ∙ (1 – ln (x + 1)) = (x + 1)1/(x + 1) – 2 ∙ (1 – ln (x + 1)).
5. x – y = arcsin x – arcsin y, y – arcsin y = x – arcsin x, (y – arcsin y)’ = (x – arcsin x)’,
y' – y’ ∙ (1 – y2)-1/2 = 1 – (1 – x2)-1/2, y’(1 – (1 – y2)-1/2) = 1 – (1 – x2)-1/2, y’ = (1 – (1 – x2)-1/2)/(1 – (1 – y2)-1/2).
6. y’t = (et ∙ cos t)’t = (et)’t ∙ cos t + et ∙ (cos t)’t = et ∙ cos t – et ∙ sin t = et ∙ (cos t – sin t),
x’t = (et ∙ sin t)’t = (et)’t ∙ sin t + et ∙ (sin t)’t = et ∙ sin t + et ∙ cos t = et ∙ (cos t + sin t),
y’x = y’t/x’t = et ∙ (cos t – sin t)/(et ∙ (cos t + sin t)) = (cos t – sin t)/(cos t + sin t).
С уважением.
Об авторе:
Facta loquuntur.