Question

У=sin x-cos x , x0=п/4

Answer 1

y' = (sin(x) - cos(x))' = (sin(x))' - (cos(x))' = cos(x) - (-sin(x)) = cos(x)+sin(x),
y'(x0) = cos(x0) + sin(x0) = cos(п/4) + sin(п/4) = ((√2)/2) + ((√2)/2) = √2.