1. Найдите производную функции: a) $f(x) = 3x^5 - 5x^2$ б) $f(x) = 3\sin x + \cos 3x - \ctg x$ в) $f(x) = (3x^2 + 1)(4x^3 - 3)$ г) $f(x) = \frac{2\sin x - 2}{\cos x}$ д) $f(x) = \sqrt{3x^2 + 1}$

a) $f(x) = 3x^5 - 5x^2$ $f'(x) = 3 \cdot 5x^4 - 5 \cdot 2x = 15x^4 - 10x$ б) $f(x) = 3\sin x + \cos 3x - \ctg x$ $f'(x) = 3\cos x - 3\sin 3x + \frac{1}{\sin^2 x}$ в) $f(x) = (3x^2 + 1)(4x^3 - 3)$ $f'(x) = (6x)(4x^3 - 3) + (3x^2 + 1)(12x^2) = 24x^4 - 18x + 36x^4 + 12x^2 = 60x^4 + 12x^2 - 18x$ г) $f(x) = \frac{2\sin x - 2}{\cos x}$ $f'(x) = \frac{(2\cos x)(\cos x) - (2\sin x - 2)(-\sin x)}{\cos^2 x} = \frac{2\cos^2 x + 2\sin^2 x - 2\sin x}{\cos^2 x} = \frac{2 - 2\sin x}{\cos^2 x} = \frac{2(1 - \sin x)}{\cos^2 x}$ д) $f(x) = \sqrt{3x^2 + 1}$ $f'(x) = \frac{1}{2\sqrt{3x^2 + 1}} \cdot 6x = \frac{3x}{\sqrt{3x^2 + 1}}$