Найдите производную функции а) y=x^3*sin(x/3) б) y=корень(1+7tg2x) в) y=cos^2(3x^2) г)...

а) $y = x^2sin\frac{x}{3}$

$y' = 3x^2sin\frac{x}{3}+x^3cos\frac{x}{3}*\frac{1}{3} = x^2(3sin\frac{x}{3}+\frac{1}{3}x*cos\frac{x}{3})$

б) $y=\sqrt{1+7tg2x}$

$y' = -\frac{1}{2\sqrt{1+7tg2x}}7\frac{2}{cos^22x}=-\frac{7}{cos^22x\sqrt{1+7tg2x}}$

в) $y = cos^2(3x^2)$

$y' = 2cos3x^2*(-sin3x^2)*6x = -12x*cos(3x^2)sin(3x^2)$

г) $y=\sqrt{cos^5\frac{x}{5}-1}$

$y' = -\frac{1}{2\sqrt{cos^5\frac{x}{5}-1}}*5cos^4\frac{x}{5}(-sin\frac{x}{5})\frac{1}{5}=$ $\frac{cos^4\frac{x}{5}sin\frac{x}{5}}{2\sqrt{cos^5\frac{x}{5}-1}}$

д) $y=\frac{x^2}{1-x^3}$

$y' = \frac{2x(1-x^3)-x^2(-3x^2)}{(1-x^3)^2}=\frac{2x+x^4}{(1-x^3)^2}$