Question

Математический диктант «Производная степенной функции»

Найдите производную функции

Answer 1

$1)9 {x}^{8} \\ 2) - 2 {x}^{ - 3} = - \frac{2}{ {x}^{3} } \\ 3)6.1 {x}^{5.1}$

$4) - 3.7 {x}^{ - 4.7} = - \frac{37}{10 {x}^{4.7} } \\$

$5) - 7 {x}^{ - 8} = - \frac{7}{ {x}^{8} } \\$

$6)( \frac{1}{ {x}^{ - 3.4} } )' = ({x}^{3.4} )' = 3.4 {x}^{2.4} \\$

$7) \frac{1}{2} {x}^{ - \frac{1}{2} } = \frac{1}{2 \sqrt{x} } \\$

$8) \frac{1}{9} {x}^{ - \frac{8}{9} } = \frac{1}{9 \sqrt[9]{ {x}^{8} } } \\$

$9) \frac{5}{3} {x}^{ \frac{2}{3} } = \frac{5}{3} \sqrt[3]{ {x}^{2} } \\$

$10)6$

$11)7 {(13x + 1)}^{6} \times 13 = 91 {(13x + 1)}^{6} \\$

$12)1.2 {(0.5 x - 10)}^{0.2} \times 0.5 = 06 {(0.5x - 10)}^{0.2} \\$

$13) - 8 {(4x + 3)}^{ - 9} \times 4 = - \frac{32}{ {(4x + 3)}^{9} } \\$

$14) - \frac{1}{2} {(6x + 1)}^{ - \frac{3}{2} } \times 6 = - \frac{3}{ \sqrt{ {(6x + 1)}^{3} } } \\$