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Задать вопрос экспертам

Консультация № 109773

17.11.2007, 00:32

0.00 руб.

0 1 1

Образование

Найти производную.
arctg(x/y)=1/2(ln(x^2+y^2))

Обсуждение

Неизвестный

17.11.2007, 01:13

общий

это ответ

Здравствуйте, Kamelia26!
(arctg(x/y))‘ = (1/2*ln(x²+y²))‘,
1/(1 + (x/y)²) * (x/y)‘ = 1/2 * 1/(x²+y²) * (x²+y²)‘,
y²/(x²+y²) * (y-xy‘)/y² = 1/2 * (2x+2yy‘)/(x²+y²),
y - xy‘ = x + yy‘,
<b>y‘ = (y-x)/(y+x)</b>.

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