Question

 y=(1-sinx)/(1+sinx) производную

Answer 1

Формулы:

$(frac{u}{v})' = frac{u'v+uv'}{v^{2}}\\ (u+/-v)'=u'+/-v'$

 

 

$y=frac{1-sinx}{1+sinx}\ y'=(frac{1-sinx}{1+sinx})'=frac{(1-sinx)'cdot(1+sinx)-(1-sinx)cdot(1+sinx)'}{(1+sinx)^{2}}=\\ =frac{-cosxcdot(1+sinx)-(1-sinx)cdot cosx}{(1+sinx)^{2}}=frac{-cosx-cosxcdot sinx-cosx+cosxcdot sinx}{(1+sinx)^{2}}=\\ =-frac{2cosx}{(1+sinx)^{2}}$