N5

а)

y = (2x^2 - 3x - 1)^8

y' = 8(2x^2 - 3x - 1)'(2x^2 - 3x -1)^7 =8(4x -3)(2x^2 - 3x - 1)^7 = (32x - 24)(2x^2 - 3x -1)^7

б)

y = x × tgx

y' = (x)'tg(x) + x(tg(x))' = tgx + x/cos^2 (x) = (0,5sin(2x) + x)/cos^2 (x)

в)

y = (x^2 - 2x -1)/x

y' = ((x^2 - 2x -1)/x)' = (x - 2 - 1/x)' = 1 + 1/x^2 = (x^2 + 1)/x^2

г)

y = 3sqrt(x^3 - 6x + 3)

y' = 3(x^3 - 6x + 3)'/2sqrt(x^3 - 6x + 3) = (9x^2 - 18)/2sqrt(x^3 - 6x + 3)

д)

y = x(x^4 - 2x -1) = x^5 - 2x^2 - x

y' = 5x^4 - 4x - 1