Question

arcsin x=2y+arccosy найти производную

Answer 1

$arcsinx=2y+arccosy; y=-arcsinx+2y+arccosy; y'=((x)'/ sqrt{1- x^{2} })+2-((y)'/ sqrt{1- y^{2} })= =1/ sqrt{1- x^{2}}+2-1/ sqrt{1- y^{2}}= 1/ sqrt{1- x^{2}}*sqrt{1- y^{2}}+2/sqrt{1- x^{2}}*sqrt{1- y^{2}}-1/sqrt{1- x^{2}}*sqrt{1- y^{2}} =2/sqrt{1- x^{2}}*sqrt{1- y^{2}}$