Найдите производную функции

1) y=cos (arctgx)

2) y=sin (arcctgx)

3) y=sin (arccosx)

4) y=cos (arcsinx)

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)