Question

Срочно зделать все даю 50 балов

Answer 1

1)

$f(x) = \frac{x}{4} \\ f'(x) = \frac{x {}^{1 - 1} }{4} = \frac{1}{4}$

2)

$f(x) = \sqrt{3} x \\ f'(x) = \sqrt{3} {x}^{1 - 1 } = \sqrt{3}$

3)

$g(x) = 4 {x}^{2} \\ g'(x) = 4 \times 2 {x}^{2 - 1} = 8x$

5)

$g(x) = {x}^{12} \\ g'(x) = 12 {x}^{12 - 1} = 12 {x}^{11}$

7)

$h(x) = {x}^{ - 6} \\ h '(x)= - 6x { }^{ - 6 - 1} = - 6 {x}^{ - 7} = - \frac{6}{ {x}^{7} }$

8)

$f(x) = - 5 {x}^{ - 8} \\ f'(x) = - 5 \times ( - 8)x {}^{ - 8 - 1} = 40 {x}^{ - 9} = \frac{40}{ {x}^{9} }$

9)

$f(x) = \frac{1}{ {x}^{7} } = {x}^{ - 7} \\ f'(x) = - 7 {x}^{ - 7 - 1} = - 7 {x}^{ - 8} = - \frac{7}{ {x}^{8} }$

10)

$h(x) = \frac{4}{ {x}^{5} } = 4 {x}^{ - 5} \\ h'(x) = - 5 \times 4x {}^{ - 5 - 1} = - 20 {x}^{ - 6} = - \frac{20}{ {x}^{6} }$

11)

$q(x) = \frac{1}{6 {x}^{6} } = \frac{1}{6} {x}^{ - 6} \\ q'(x) = - 6 \times \frac{1}{6} {x}^{ - 6 - 1} = - {x}^{ - 7} = - \frac{1}{ {x}^{7} }$

12)

$g(x) = \frac{2}{9 {x}^{3} } = \frac{2}{9} {x}^{ - 3} \\ g'(x) = - 3 \times \frac{2}{9} {x}^{ - 3 - 1} = - \frac{2}{3} {x}^{ - 4} = - \frac{2}{3 {x}^{4} }$