Найти производную функции: а) y = (arcsin3x-cos5x+3x) 27/8 б) y=4^ (ln5x-2x+e^3x) в) y=tg (15x-8) / ln (14x+3) г) y=ln6 корень из5x^3+1/5x^3+3 д) y = (x^3 - 2) ^ln^ (3x-8)

y' = (3sin (x^9 - sin x) + 7) ' = (3sin (x^9 - sin x)) ' + (7) ' = (x^9 - sin x) ' * (3sin (x^9 - sin x)) ' + (7) ' = ((x^9) - (sin x) ') * (3sin (x^9 - sin x)) ' + (7) ' = ((9x^8) - cos x) * 3cos (x^9 - sin x) + 0 = ((9x^8) - cos x) * 3cos (x^9 - sin x).

y' = (ln x + x^2 * sin (1 / x)) ' = (ln x) ' + (x^2 * sin (1 / x)) ' = (ln x) ' + ((x^2) ' * sin (1 / x)) + (x^2 * (sin (1 / x)) ' = (1 / х) + 2x * sin (1 / x) + x^2 * (-cos (1 / x)) / x^2 = (1 / х) + 2x * sin (1 / x) - (cos (1 / x)).

f (x) ' = (sin^2 (2φ)) ' = (2φ) ' * (sin (2φ)) ' * (sin^2 (2φ)) ' = 2 * (cos (2φ) * 2sin (2φ) = 4 (cos 2φ) (sin 2φ).