У=sin x-cos x, x0=п/4

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.