2.1 Derivatives

1.

(a) 0 (b) $${\frac{1}{2\sqrt{x-1}}}$$ (c) $${-\frac{2}{x^{3}}}$$

2.

(a) $1$ (b) $-6$

3.

(a) $y = -x - 1$ (b) $y = -12x + 21$ (c) $${y = \frac{1}{4}x + 1}$$

4.

(a) $${y' = 55x^{4} - 18x^{2}}$$ (b) $${y' = \frac{2}{x^{3}}}$$ (c) $${y' = 3x^{2} - 6x - 1}$$ (d) $${y' = -\frac{1}{(x-2)^{2}}}$$

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