Question

Учителя Светила Прошу!!!!!!сделайте 540

Answer 1

$f(x)= \frac{Cos ^{2}x }{1+Sin ^{2}x } \\\\f'(x)= \frac{(Cos ^{2}x)'*(1+Sin ^{2}x)-Cos ^{2}x*(1+Sin ^{2} x)}{(1+Sin ^{2}x) ^{2} } =$$\frac{2Cosx*(Cosx)'*(1+Sin ^{2}x)-Cos ^{2}x*2Sinx*(Sinx)' }{(1+Sin ^{2}x) ^{2} } =$ \frac{-2CosxSinx(1+Sin ^{2} x)-2Cos ^{3} xSinx}{(1+Sin ^{2}x) ^{2} }[/tex] =[/tex] \frac{-2CosxSinx-2CosxSin ^{3}x-2Cos ^{3} xSinx }{(1+Sin ^{2}x) ^{2} } [/tex] \frac{-2CosxSinx(1+Sin ^{2}x+Cos ^{2} x) }{(1+Sin ^{2}x) ^{2} } = \frac{-4CosxSinx}{(1+Sin ^{2} x) ^{2} }\\\\f( \frac{ \pi }{4}) = \frac{Cos ^{2} \frac{ \pi }{4} }{1+Sin ^{2} \frac{ \pi }{4} } = \frac{( \frac{1}{ \sqrt{2} }) ^{2} }{1+( \frac{1}{ \sqrt{2} }) ^{2} }= \frac{ \frac{1}{2} }{ \frac{3}{2} }= \frac{1}{3}\\\\f'( \frac{ \pi }{4}) = \frac{-4*Cos \frac{ \pi }{4} Sin \frac{ \pi }{4} }{(1+Sin ^{2} \frac{ \pi }{4}) ^{2} } = [/tex]$\frac{-4* \frac{1}{ \sqrt{2} }* \frac{1}{ \sqrt{2} } }{[1+( \frac{1}{ \sqrt{2} }) ^{2}] ^{2} }= \frac{-2}{( \frac{3}{2}) ^{2} } = \frac{-2}{ \frac{9}{4} }=- \frac{8}{9} \\\\f( \frac{ \pi }{4})-3f'( \frac{ \pi }{4} ) = \frac{1}{3}-3*(- \frac{8}{9})= \frac{1}{3}+ \frac{8}{3}= \frac{9}{3}=3$

Answer 2

!!!!!!!!!!!!!!!!!!!!!!!