Question

Найдите производную срочно! 75 баллов! ​

Answer 1

Ответ:

$1)f'(x) = \frac{3 \times 6}{4} {x}^{5} - 6 {x}^{ - 4} - \frac{1}{4} \times \frac{1}{2} {x}^{ - \frac{1}{2} } = \\ = \frac{9}{2} {x}^{5} - \frac{6}{ {x}^{4} } - \frac{1}{8 \sqrt{x} }$

$2)f'(x) = \frac{7}{3} \times 3 {x}^{2} - 3 {x}^{ - 2} = \\ = 7 {x}^{2} - \frac{3}{ {x}^{2} }$

$3)f'(x) = 1 \times (x + 2) + 1 \times (x - 8) = 2x - 6$

$4)f'(x) = \frac{1 \times (x - 4) - 1 \times (x + 5)}{ {(x - 4)}^{2} } = \\ = \frac{x - 4 - x - 5}{ {(x - 4)}^{2} } = - \frac{9}{ {(x - 4)}^{2} }$

$5)f'(x) = 3 {x}^{2} (2x + 3) + 2( {x}^{3} - 1) = \\ = 6 {x}^{3} + 9 {x}^{2} + 2 {x}^{3} + 2 = 8 {x}^{3} + 9 {x}^{2} + 2$

$6)f'(x) = \frac{(2x + 2) {x}^{3} - 3 {x}^{2}( {x}^{2} + 2x - 3) }{ {x}^{6} } = \\ = \frac{2 {x}^{4} + 2 {x}^{3} - 3 {x}^{4} - 6 {x}^{3} + {x}^{2} }{ {x}^{6} } = \\ = \frac{ - {x}^{4} - 4 {x}^{3} + {x}^{2} }{ {x}^{6} } = \frac{ {x}^{2}(1 - {x}^{2} - 4x) } { {x}^{6} } = \\ = \frac{1 - {x}^{2} - 4x }{ {x}^{4} }$

$7)f'(x) = \frac{1}{2} {(3 {x}^{2} - 8x)}^{ - \frac{1}{2} } \times (6x - 8) = \\ = \frac{2(3x - 4)}{2 \sqrt{3 {x}^{2} - 8x } } = \frac{3x - 4}{ \sqrt{3 {x}^{2} - 8x } }$

$8)f'(x) = 4 {x}^{3} - 15 {x}^{2}$

$9)f'(x) = 2x(3x - 7) + 3( {x}^{2} - 1) = \\ = 6 {x}^{2} - 14x + 3 {x}^{2} - 3 = \\ = 9 {x}^{2} - 14x - 3$

$10)f'(x) = 6 {x}^{7} - 6 {x}^{ - 3} - \frac{1}{6} \times \frac{1}{2} {x}^{ - \frac{1}{2} } = \\ = 6 {x}^{7} - \frac{6}{ {x}^{3} } - \frac{1}{12 \sqrt{x} }$

$11)f'(x) = \frac{(3 {x}^{2} - 4)x - ( {x}^{3} - 4x + 3) }{ {x}^{2} } = \\ = \frac{3 {x}^{3} - 4x - {x}^{3} + 4x - 3 }{ {x}^{2} } = \\ = \frac{2 {x}^{3} + 3 }{ {x}^{2} }$

$12)f'(x) = \frac{13}{3} \times 3 {x}^{2} - {x}^{ - 2} = \\ = 13 {x}^{2} - \frac{1}{ {x}^{2} }$

$13)f'(x) = \frac{1}{2} {(8 + 4x)}^{ - \frac{1}{2} } \times 4 = \\ = \frac{2}{ \sqrt{8 + 4x} }$

$14)f'(x) = x + 1 + x - 5 = 2x - 4$

$15)f'(x) = \frac{1}{2 \sqrt{3 {x}^{2} - 8x} } \times (6x - 8) = \\ = \frac{3x - 4}{ \sqrt{3 {x}^{2} - 8x} }$

$16)f'(x) = \frac{2(x - 4) - (2x + 5)}{ {(x - 4)}^{2} } = \\ = \frac{2x - 8 - 2x - 5}{ {(x - 4)}^{2} } = \\ = - \frac{13}{ {(x - 4)}^{2} }$

$17)f'(x) = 1 \times \sqrt{3 - 4 x} + \frac{1}{2} {(3 - 4x)}^{ - \frac{1}{2} } \times ( - 4) \times x = \\ = \sqrt{3 - 4x} - \frac{2x}{ \sqrt{3 - 4x} }$