Найдите производную функции в точке $$x_0$$: a) $$y = x^6, x_0 = -2$$; б) $$y = \frac{-8}{x}, x_0 = 4$$; в) $$y = 6 - 3x, x_0 = 5$$; г) $$y = 15\sqrt{x}, x_0 = 25$$.

a) $$y = x^6$$, $$x_0 = -2$$ $$y' = 6x^5$$ $$y'(-2) = 6*(-2)^5 = 6*(-32) = -192$$ б) $$y = \frac{-8}{x} = -8x^{-1}$$, $$x_0 = 4$$ $$y' = 8x^{-2} = \frac{8}{x^2}$$ $$y'(4) = \frac{8}{4^2} = \frac{8}{16} = \frac{1}{2}$$ в) $$y = 6 - 3x$$, $$x_0 = 5$$ $$y' = -3$$ $$y'(5) = -3$$ г) $$y = 15\sqrt{x} = 15x^{\frac{1}{2}}$$, $$x_0 = 25$$ $$y' = 15 * \frac{1}{2}x^{-\frac{1}{2}} = \frac{15}{2\sqrt{x}}$$ $$y'(25) = \frac{15}{2\sqrt{25}} = \frac{15}{2*5} = \frac{15}{10} = \frac{3}{2}$$