Question

найдите производную функции
1) y=cos(arctgx)
2) y=sin(arcctgx)
3) y=sin(arccosx)
4) y=cos(arcsinx)

Answer 1

1) y'= -sin(arctgx)*(arctgx)' = - sin(arctgx)*1/(1+x²)
2) y'= cos(arcctgx)*(arcctgx)' =cos(arctgx)*(-1/(1+x²)) = -cos(arctgx)*1/(1+x²)
3) y'= cos(arccosx)*(arccosx)' =cos(arccosx)*(-sqrt(1-x²))= - cos(arccosx)*sqrt(1-x²)
4) y'= - sin(arcsinx)*(arcsinx)' = - sin(arcsinx)*sqrt(1-x²)