Chapter 3 - Derivatives - 3.5 Derivatives of Trigonometric Functions - 3.5 Exercises - Page 169: 17

$y' = cos (x) - sin (x)$

$y = sin (x) + cos (x)$ $y' = (sin (x) + cos (x))' = (sin (x))' + (cos (x))'$ $(sin (x))' = cos(x)$ $(cos (x))' = - sin(x)$ Therefore $y' = (sin (x) + cos (x))' = (sin (x))' + (cos (x))' = cos (x) - sin (x)$