y= sin^2 3x × sin 3x^2
Обчислить складную производную

Ответ:

6sin9x^3×cos3x + sin^2 3x × cos18x^2

Пошаговое объяснение:

y = sin^2 3x × sin3x^2

y ` = (sin^2 3x × sin3x^2) ` = (sin^2 3x) ` × (sin3x^2) + (sin^2 3x) × (sin3x^2) ` = 2sin3x × (sin3x) ` × (sin3x^2) + (sin^2 3x) × (cos3x × 3 × 2x) = (2sin3x × cos3x × 3) × (sin3x^2) + (sin^2 3x) × (cos3x × 3 × 2x) = (6sin3xcos3x) × (sin3x^2) + (sin^2 3x) × (cos3x × 6x) = 6sin9x^3×cos3x + (sin^2 3x) × (cos18x^2) = 6sin9x^3×cos3x + sin^2 3x × cos18x^2