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© Максимовская М.А., 2009 год, Центр образования №109.
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h ( x ) = g ( f ( x )) z = h ( x ) = 1 – x 2 y = f ( x ) =1 – x 2 z = g ( y ) = y
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Дано: f(x) = 3 - 2x g(x) = x 2 p(x) = sin x Найти: а) h(x) = g(f(x)) б) h(x) = p(f(x)) Решение: а) f(x) = 3 - 2x g(f(x)) = (3 - 2x) 2 Ответ: h(x) = (3 - 2x) 2 б) f(x) = 3 - 2x p(f(x)) = sin (3 - 2x) Ответ: h(x) = sin (3 – 2x)
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h' ( x 0 ) = h ( x ) = g ( f ( x )) g' ( f ( x 0 )) f ' (x0)f ' (x0)f ' (x0)f ' (x0) f(x) = (2x – 7) 8 f '(x) = ((2x – 7) 8 )' = 8(2x – 7) 7 (2x – 7)' = 8(2x – 7) 7 ∙ 2 = 16(2x – 7) 7
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(sin x )' = cos x (cos x )' = - sin x (tg x )' = cos 2 x 1 (ctg x )' = - sin 2 x 1
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(sin 2 (3 x – 1))' = 2sin(3 x – 1) (sin(3 x – 1))' = 2sin(3 x – 1) cos(3 x – 1) (3 x – 1)' = 2sin(3 x – 1) cos(3 x – 1) ∙ 3 = 3sin(6 x – 2)
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