Решите с объяснением — вопрос №2874674

Ответ

Автор - mursalovasuriya

Ответ:

$1) {({4}^{x})}^{l} = {4}^{x} ln(4) \ {({x}^{- 2} )}^{l} = - 2 times {x}^{ - 2 - 1} = - 2 {x}^{ - 3} \ y = {4}^{x} ln(4) - 2 {x}^{ - 3}$

$2){( {3}^{x} )}^{l} = {3}^{x} ln(3) \ {( {2x}^{ - 2}) }^{l} = 2 times ( -2) times {x}^{ - 2 - 1} = - 4 {x}^ {- 3} \ {(3 log_{2}(x) )}^{l} = frac{3}{x ln(2) } \ {f}^{l} (x) = {3}^{x} ln(3) - frac{4}{ {x}^{3} } + frac{3}{x ln(2) }$

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

$4){f}^{l} (x) = frac{2 times 2 {x}^{2 - 1} ( {x}^{3} + 3 ) - 2 {x}^{2} times 3 times {x}^{3 - 1} }{ {( {x}^{3} + 3 )}^{2} } \ frac{4x( {x}^{3} + 3) - 6 {x}^{4} }{ {( {x}^{3} + 3)}^{2} } = \ = frac{12x - 2 {x}^{4} }{ {( {x}^{3} + 3 )}^{2} }$

$5) {f}^{l} (x) ={ ((5x + 2)2cosx) }^{l} = \ = { ((10x cosx + 4cosx) }^{l} \ \ {(10xcosx) }^{l} = 10cosx + 10x times ( - sinx) = \ = 10cosx - 10xsinx \ \ {(4 cosx)}^{l} = - 4sinx \ \ {f}^{l} (x) =10cosx - 10xsinx - 4sinx$