f(x)= sinx*(cosx-1)f(x) =x^2 * ctgxf(x)= cosx(1+sinx) f(x)=x^2 * tgx Найти производные

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).