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Консультация № 173679
25.10.2009, 20:38
25.00 руб.
0
1
1
Здравствуйте! Помогите пожалуйста найти производные
1. y= (1+x)/корень из (1-x)
2. y=(Ln^2) * (x^2)
3. y= (1-cosx)/(1+cosx) и всё это под корнем
4. y= (e^(x/a)*(cos^(x/a)
5. y=((1+sin^2(x)) * ((1+cos^2(x))
Заранее спасибо!
1. y= (1+x)/корень из (1-x)
2. y=(Ln^2) * (x^2)
3. y= (1-cosx)/(1+cosx) и всё это под корнем
4. y= (e^(x/a)*(cos^(x/a)
5. y=((1+sin^2(x)) * ((1+cos^2(x))
Заранее спасибо!
Обсуждение
Неизвестный
25.10.2009, 20:59
общий
это ответ
Здравствуйте, Галина Викторовна.
1)[(1+x) / √(1-x)]' = [(1+x)'*√(1-x) - (√(1-x))'*(1+x)] / (√(1-x))2=[√(1-x) + (1+x)/(2*√(1-x))] / (1-x) = [2*(1-x)+(1+x)] / (2(1-x)√(1-x)) = (3-x)/[2*(1-x)*√(1-x)]
2)y=Ln2 (x2)
y'=2*ln(x2)*(lnx2)'= 2*ln(x2) / x2 * (x2)' = 2*ln(x2) / x2 * 2 *x = 4*ln(x2)/x
5)y=((1+sin^2(x)) * ((1+cos^2(x))
y'= (1+2*sinx*cosx)*(1+cos2x) + (1+sin2x)*(1+2*cosx*(-sinx))=1+cos2x+2*sinx*cosx+2*sinx*cos3x +
+ 1-2sinxcosx+sin2x-2cosx*sin3x=2+2*sinx*cos3x -2cosx*sin3x + cos2x + sin2x =
=3 +2sinx*cosx*(cos2x-sin2x) = 3+sin2x * cos(2x) = 3+sin(4x)/2
1)[(1+x) / √(1-x)]' = [(1+x)'*√(1-x) - (√(1-x))'*(1+x)] / (√(1-x))2=[√(1-x) + (1+x)/(2*√(1-x))] / (1-x) = [2*(1-x)+(1+x)] / (2(1-x)√(1-x)) = (3-x)/[2*(1-x)*√(1-x)]
2)y=Ln2 (x2)
y'=2*ln(x2)*(lnx2)'= 2*ln(x2) / x2 * (x2)' = 2*ln(x2) / x2 * 2 *x = 4*ln(x2)/x
5)y=((1+sin^2(x)) * ((1+cos^2(x))
y'= (1+2*sinx*cosx)*(1+cos2x) + (1+sin2x)*(1+2*cosx*(-sinx))=1+cos2x+2*sinx*cosx+2*sinx*cos3x +
+ 1-2sinxcosx+sin2x-2cosx*sin3x=2+2*sinx*cos3x -2cosx*sin3x + cos2x + sin2x =
=3 +2sinx*cosx*(cos2x-sin2x) = 3+sin2x * cos(2x) = 3+sin(4x)/2
Форма ответа
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