A====== y = x^5/5 - 2/(3x^3) + x - 7 y' = ( x^5/5)' - (2/3x^3)' + (x)' - (7)' ( x^5/5)' = 5x^4/5 = x^4 (2/3x^3)' = 2/3 * x^-3 = 2/3 * -3x^-4 = -2 x^-4 = 2/x^4 (x)' = 1 (7)' = 0 y' = x^4 + 2/x^4+1 б=======y = корень из x-tgx/2+x^2cos2x y' = (корень из x) ' - (tgx/2)' + (x^2cos2x)' (корень из x) ' = 1/(2 корень из x) (tgx/2)' = 1/2*sec^2x = 1/(2cos^2x) ( (tgx)' = sec^2x= 1/cos^2x ) (x^2*cos2x)' = x^2* (cos2x)'+ cos2x * (x^2)' (cos2x)' = -2sin2x (сложная функция, где Z = 2x, (2x)' = 2 cos x = - sin x) (x^2)' = 2x (x^2*cos2x)' = x^2*(-2sin2x)+cos2x*2x = 2x*cos2x - 2x^2sin2x y' = 1/(2 корень из x) - 1/(2cos^2x) + 2x*cos2x - 2x^2sin2x в================= y=(1+sinx)/(1-cosx) y' = [ (1-cosx) * (1+sinx)' - (1+sinx) * (1-cosx)' ] / (1-cosx)^2 (по формуле (u/v)' = (vu'-uv')/v^2 ) (1+sinx)' = cos x (1-cosx)' = sinx (cosx = - sin x) y' = [ (1-cosx) * cosx - (1+sinx) * sin x ] / (1-cos x)^2 сократим немного [ (1-cosx) * cosx/(1-cos x)^2 ] - [(1+sinx) * sin x / (1-cos x)^2] = = [cosx/1-cos x] - [(1+sinx) * sin x / (1-cos x)^2]