Question

Вычислите производную функций
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Answer 1

1.

$( {x}^{12} )' = 12 {x}^{11}$

$( {x}^{45} )' = 45 {x}^{44}$

$( {x}^{ - 25} )' = - 25 {x}^{ - 26} = - \frac{25}{ {x}^{26} }$

$(3 {x}^{14} )' = 42 {x}^{13}$

$( \frac{ {x}^{9} }{3} )' = 3 {x}^{8}$

$( \frac{7 {x}^{4} }{2} ) = \frac{7}{2} \times 4 {x}^{3} =14 {x}^{3}$

$( \frac{6 {x}^{5} }{5} ) '= 6 {x}^{4}$

2.

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

$( \frac{ 5 }{ {x}^{5} } ) '= (5 {x}^{ - 5} ) = - 25 {x}^{ - 6} = - \frac{25}{ {x}^{6} }$

$( \frac{3}{4} {x}^{ - 4} ) '= - 3 {x}^{ - 5} = - \frac{3}{ {x}^{5} }$

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

$( \frac{1}{3} {x}^{ - 6} ) '= - \frac{1}{2} {x}^{ - 7} = - \frac{1}{2 {x}^{7} }$

$( \frac{4}{33} {x}^{ - 11} ) '= \frac{4 \times ( - 11)}{33} {x}^{ - 12} = \\ = - \frac{4}{3 {x}^{12} }$

3.

$a)7 {x}^{6} + 12 {x}^{3} - 10x - 1$

б)

$20 {x}^{9} - 8 {x}^{7} + 9 {x}^{2}$

в)

${x}^{3} + 9 {x}^{2} + 4 {x}^{ - 3} + 5 = \\ = {x}^{3} + 9 {x}^{2} + \frac{4}{ {x}^{3} } + 5$