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Консультация № 161648
01.03.2009, 00:00
0.00 руб.
0
1
1
Здравствуйте! Помогите пожалуйста найти производные следующих функций:
а) 1/(1-2x);
б) e^[arcctg(^3)√x];
в) 3xsin(x/3);
г) x/[x(^3)+1];
д) ln{√[(1-x^2)/(1+x^2)]}
а) 1/(1-2x);
б) e^[arcctg(^3)√x];
в) 3xsin(x/3);
г) x/[x(^3)+1];
д) ln{√[(1-x^2)/(1+x^2)]}
Обсуждение
Неизвестный
01.03.2009, 17:41
общий
это ответ
Здравствуйте, Орехов Роман Александрович!
а) [1/(1-2x)]'=2/(1-2x)^2
б) (e^[arcctg(^3)√x])'=e^[arcctg(^3)√x] * 3arcctg(^2)√x * 1/(1+х) * 1/(2√x)=3/(2√x(1+х) * arcctg(^2)√x * e^[arcctg(^3)√x]
в) (3xsin(x/3))'=3sin(x/3)+3x*1/3*cos(x/3)=3sin(x/3)+xcos(x/3)
г) (x/[x(^3)+1])'=(x^3+1-3x^3)/(x^3+1)^2=(1-2x^3)/(x^3+1)^2
д) ( ln{√[(1-x^2)/(1+x^2)]} )'=√[(1+x^2)/(1-x^2)] * √[(1+x^2)/(1-x^2)]/2 * (-2x(1+x^2)-2x(1-x^2))/(1+x^2)^2=-2x/(1-x^4)
а) [1/(1-2x)]'=2/(1-2x)^2
б) (e^[arcctg(^3)√x])'=e^[arcctg(^3)√x] * 3arcctg(^2)√x * 1/(1+х) * 1/(2√x)=3/(2√x(1+х) * arcctg(^2)√x * e^[arcctg(^3)√x]
в) (3xsin(x/3))'=3sin(x/3)+3x*1/3*cos(x/3)=3sin(x/3)+xcos(x/3)
г) (x/[x(^3)+1])'=(x^3+1-3x^3)/(x^3+1)^2=(1-2x^3)/(x^3+1)^2
д) ( ln{√[(1-x^2)/(1+x^2)]} )'=√[(1+x^2)/(1-x^2)] * √[(1+x^2)/(1-x^2)]/2 * (-2x(1+x^2)-2x(1-x^2))/(1+x^2)^2=-2x/(1-x^4)
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