Question

найти производную
$y = {e}^{sin^{2}2x}$
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Answer 1

Ответ:

${y}^{ | } ( \frac{\pi}{8}) = 2 \sqrt{e}$

Пошаговое объяснение:

$y^{ | } = ({e}^{ {sin}^{2}2x })^{ | } = {e}^{ {sin}^{2}2x} \times {( {sin}^{2}2x) }^{ | } = {e}^{ {sin}^{2} 2x} \times 2sin2x \times {(sin2x)}^{ | } = {e}^{ {sin}^{2}2x} \times 2sin2x \times cos2x \times {(2x)}^{ | } = {e}^{ {sin}^{2}2x} \times (2sin2 {x \times cos2x)} \times 2 = 2 {e}^{ {sin}^{2}2x} \times sin4x$

${y}^{ |}( \frac{\pi}{8} ) = 2 \times {e}^{ {sin}^{2}(2 \times \frac{\pi}{8}) } \times sin (4 \times \frac{\pi}{8}) = 2 \times {e}^{ {sin}^{2} \frac{\pi}{4}} \times sin \frac{\pi}{2} = 2 \times {e}^{ {( \frac{ \sqrt{2} }{2}) }^{2} } \times 1 = 2 \times {e}^{ \frac{1}{2} } = 2 \sqrt{e}$