Question

Кто сможет решить?(( Найти производную 1-15

Answer 1

$1)y' = 9 {x}^{8}$

$2)y' = - 12 {x}^{ - 13} = \frac{ - 12}{ {x}^{13} }$

$3)y' = \frac{4}{5} {x}^{ - \frac{1}{5} } = \frac{4}{5 \sqrt[5]{x} }$

$4)y' = - \frac{2}{3} {x}^{ - \frac{5}{3} } = - \frac{2}{3x \sqrt[3]{ {x}^{2} } }$

$5)y' = - 18 {x}^{ - 19} = - \frac{18}{ {x}^{19} }$

$6)y' = \frac{1}{4} {x}^{ - \frac{3}{4} } = \frac{1}{4 \sqrt[4]{ {x}^{3} } }$

$7)y' = - \frac{5}{6} {x}^{ - \frac{11}{6} } = - \frac{5}{6x \sqrt[6]{ {x}^{5} } }$

$8)y' = 4 {(2 - 5x)}^{3} \times ( - 5) = - 2 0 {(2 - 5x)}^{3}$

$9)y' = 5 {( - 2x)}^{4} \times ( - 2) = - 10 {( - 2x)}^{4} = - 10 \times 16 {x}^{4} = - 160 {x}^{4}$

$10)y' = - 4 {(7x - 1)}^{ - 5} \times 7 = \frac{ - 28}{ {(7x - 1)}^{5} }$

$11)y' = \frac{1}{10} {( - 3 + 12x)}^{ \frac{ - 9}{10} } \times 12 = \frac{3}{2 \sqrt[10]{ {(12x - 3)}^{9} } }$

$12)y' = - \frac{5}{6} {( \frac{x}{3} + 2)}^{ - \frac{11}{6} } \times \frac{1}{3} = - \frac{5}{18 \sqrt[6]{ {( \frac{x}{3} + 2) }^{11} } }$

$13)y' = - 4 {x}^{ - 5} = - \frac{4}{ {x}^{5} } \\ y'(2) = - \frac{4}{32} = - \frac{1}{8}$

$14)y' = \frac{1}{2} {(1 - 5x)}^{ - \frac{1}{2} } \times ( - 5) = - \frac{5}{2 \sqrt{1 - 5x} } \\ y'( - 3) = - \frac{5}{2 \sqrt{1 + 15} } = - \frac{5}{2} \times \frac{1}{4} = - \frac{5}{8}$

$15)f'(x) = 5 {x}^{4} \\ 5 {x}^{4} = 5 \\ {x}^{4} = 1 \\ x = + - 1$