Задача 71920 Найти производную y = (1/ 3sqrt(cos^6...
Условие
y = (1/ 3sqrt(cos^6 (sqrt(2) - sin^2*4x)
математика ВУЗ
77
Решение
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[m]y=cos^{-2}(\sqrt{2}-sin^24x)[/m]
По формуле [m](u^{-2})`=-2 u^{-3}\cdot u`[/m]
[m]y`=-2cos^{-3}(\sqrt{2}-sin^24x)\cdot (\sqrt{2}-sin^24x)`[/m]
[m]y`=-\frac{2}{cos^{3}(\sqrt{2}-sin^24x)}\cdot((\sqrt{2})`-2\cdot sin4x\cdot (sin4x)`)[/m]
[m]y`=-\frac{2}{cos^{3}(\sqrt{2}-sin^24x)}\cdot(0-2\cdot sin4x\cdot (cos4x)\cdot (4x)`)[/m]
[m]y`=-\frac{2}{cos^{3}(\sqrt{2}-sin^24x)}\cdot(-2\cdot sin4x\cdot (cos4x)\cdot (4))[/m]
[m]y`=\frac{8\cdot sin4x\cdot cos4x}{cos^{3}(\sqrt{2}-sin^24x)}[/m]
[m]y`=\frac{4\cdot sin8x}{cos^{3}(\sqrt{2}-sin^24x)}[/m]- о т в е т