Question

Помогите пожалуйста!
3, 4

Answer 1

$f(x)= frac{ sqrt{5}x+7x^3 }{x+2} +mathrm{tg}x \ f'(x)= frac{( sqrt{5}x+7x^3)'(x+2)-( sqrt{5}x+7x^3)(x+2)' }{(x+2)^2} +(mathrm{tg}x)'= \ =frac{( sqrt{5}+21x^2)(x+2)-( sqrt{5}x+7x^3) }{(x+2)^2} + frac{1}{cos^2x}$
$f'(2)= frac{( sqrt{5}+21cdot2^2)(2+2)-( 2sqrt{5}+7cdot2^3) }{(2+2)^2} + frac{1}{cos^22} = \ =frac{4cdot( sqrt{5}+21cdot4)-( 2sqrt{5}+7cdot8) }{4^2} + frac{1}{cos^22} = frac{4cdot( sqrt{5}+84)- 2sqrt{5}-56 }{16} + frac{1}{cos^22} = \ =frac{4sqrt{5}+336- 2sqrt{5}-56 }{16} + frac{1}{cos^22} =frac{2sqrt{5}+280}{16} + frac{1}{cos^22} =frac{sqrt{5}+140}{8} + frac{1}{cos^22}$

$f(x)=cos^23x+3x^2 \ f'(x)=2cos3xcdot(cos3x)'+6x=2cos3xcdot(-sin3x)cdot(3x)'+6x= \ =-2cos3xcdotsin3xcdot3+6x=-3sin6x+6x \ f'(2)=-3sin(6cdot2)+6cdot2=-3sin12+12$