Найдите производную функции: a) $$y = 4\cos x - \frac{7}{x}$$; б) $$y = 3x \cdot \sin x$$; в) $$y = \frac{3x^2 - x}{2x}$$; г) $$y = (7x + 4)^5$$; д) $$y = \sqrt{9 - 6x}$$.

a) $$y = 4\cos x - \frac{7}{x} = 4\cos x - 7x^{-1}$$ $$y' = -4\sin x + 7x^{-2} = -4\sin x + \frac{7}{x^2}$$ б) $$y = 3x \cdot \sin x$$ $$y' = 3\sin x + 3x\cos x$$ в) $$y = \frac{3x^2 - x}{2x} = \frac{x(3x - 1)}{2x} = \frac{3x - 1}{2} = \frac{3}{2}x - \frac{1}{2}$$ $$y' = \frac{3}{2}$$ г) $$y = (7x + 4)^5$$ $$y' = 5(7x + 4)^4 * 7 = 35(7x + 4)^4$$ д) $$y = \sqrt{9 - 6x} = (9 - 6x)^{\frac{1}{2}}$$ $$y' = \frac{1}{2}(9 - 6x)^{-\frac{1}{2}} * (-6) = -3(9 - 6x)^{-\frac{1}{2}} = \frac{-3}{\sqrt{9 - 6x}}$$