вычислить производные y=(cos(3x))/(sin^2(3x)). Created by hamidullinaajn. matematika-ru

Ответ:Пошаговое объяснение:

(sin^2(3x))...

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Ответ:

$y=\frac{cos3x}{sin^23x}\\ y'=\frac{-sin3x*3*sin^23x-cos3x*2sin3x*cos3x*3}{sin^43x}=\frac{-3sin^33x-3cos3x*sin6x}{sin^43x}$

Пошаговое объяснение:

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$y=\frac{cos3x}{sin^23x}\\\\y'=\frac{-3\, sin3x\cdot sin^23x-cos3x\cdot 2\, sin3x\cdot cos3x\cdot 3}{sin^43x}=\frac{-3sin^33x-6\, sin3x\cdot cos^23x}{sin^43x}=\\\\=\frac{-3\, sin^23x-6\, cos^23x}{sin^33x}=\frac{-3\, (sin^23x+\, cos^23x)-3cos^23x}{sin^33x}=\frac{-3-3cos^23x}{sin^33x}=\\\\=\frac{-3\, (1+cos^23x)}{sin^33x}$

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