Question

ооочень надо, заранее спасибо​

Answer 1

Ответ:

$2^{cosx+1} =-ln2*2^{cosx+1}*sinx\\0,5^{1+sinx}= -ln2*2^{-1-sinx}*cosx\\cos\sqrt[3]{x+2} =-\frac{sin\sqrt[3]{x+2} }{3\sqrt[3]{(x+2)^{2} } } \\\sqrt{x^{2}+2x-1 } =\frac{x+1}{\sqrt{x^{2}+2x-1 } } \\\sqrt[3]{sinx} =\frac{cosx}{3\sqrt[3]{(sinx)^{2} } } \\\frac{1+cosx}{sinx} =-\frac{(csc\frac{x}{2})^{2} }{2} \\\frac{\sqrt{3x} }{3^{x} +1} =\frac{3^{x+1} +3-2ln3*3^{x+1} *x}{2\sqrt{3x} *(3^{x}+1)^{2} }$

Ужас,а не примеры)

Answer 2

Ответ:

13

$y = {2}^{ \cos(x) + 1}$

$y '= ln(2) \times {2}^{ \cos(x) + 1 }\times( \cos(x) + 1)' = \\ = ln(2) \times {2}^{ \cos(x) } \times ( - \sin(x))$

14

$y = {0.5}^{1 + \sin(x) }$

$y '= ln(0.5) \times {0.5}^{1 + \sin(x) } \times (1 + \sin(x) ) '= \\ = ln(0.5) \times {(0.5})^{1 + \sin(x) } \times \cos(x)$

15

$y = \cos( \sqrt[3]{x + 2} )$

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

16

$y = \sqrt{ {x}^{2} + 2x - 1 } = {( {x}^{2} + 2x - 1) }^{ \frac{1}{2} }$

$y' = \frac{1}{2} {( {x}^{2} + 2x - 1)}^{ - \frac{1}{2} } \times ( {x}^{2} + 2x - 1)' = \\ = \frac{1} {2 \sqrt{ {x}^{2} + 2x - 1} } \times (2x + 2) = \frac{x + 1}{?2 \sqrt{ {x}^{2} + 2x - 1} }$

17

$y = \sqrt[3]{ \sin(x) } \times ( \sin(x)) ^{ \frac{1}{3} }$

$y' = \frac{1}{2} {( \sin(x) )}^{ - \frac{2}{3} } \times ( \sin(x)) '= \\ = \frac{ \cos(x) }{3 \sqrt[3]{ \sin ^{2} (x) } }$

18

$y = \frac{1 + \cos(x) }{ \sin(x) }$

$y '= \frac{(1 + \cos(x))' \times \sin(x) - (\sin(x))' \times (1 + \cos(x)) }{ { \sin }^{2}(x) } = \\ = \frac{ - \sin(x) \times \sin(x) - \cos(x)(1 + \cos(x)) }{ \sin ^{2} (x) } = \\ = \frac{ - { \sin }^{2}(x) - \cos(x) - { \cos }^{2} (x)}{ { \sin }^{2}(x) } = \\ = \frac{ - 1 - \cos(x) }{ { \sin }^{2}(x) }$

19

$y = \frac{ \sqrt{3x} }{ {3}^{x} + 1} = \sqrt{3} \times \frac{ \sqrt{x} }{ {3}^{x} + 1 }$

$y '= \sqrt{3} \times \frac{( \sqrt{x} )'( {3}^{x} + 1) - ( {3}^{x} + 1)' \times \sqrt{x} }{ {( {3}^{x} + 1 )}^{2} } = \\ = \sqrt{3} \times \frac{ \frac{1}{2 \sqrt{x} } ( {3}^{x} + 1) - ln(3) \times {3}^{x} \sqrt{x} }{ {( {3}^{x} + 1)}^{2} } = \\ = \sqrt{3} \times ( \frac{1}{2 \sqrt{x} ( {3}^{x} + 1)} - \frac{ \sqrt{x} \times {3}^{x} ln(3) }{ {( {3}^{x} + 1)}^{2} } )$