#### Answer

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

#### Work Step by Step

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