1) Вычислить производную от функции эй:

a) y=9sinx+cosx*tgx

Б) y=ctgx/tgx

2) вычислить производную сложной функции:

Y=sin (x^5-8x^3+5x)

A) y' = (9sinx+cosx*tgx) '=9cosx + (cosx) '*tg (x) + cos (x) * (tgx) '=9cosx-sinx*tgx+cosx/cos^2 (x) = (9cos^2 (x) - sin^2 (x) + 1) / cosx = (9cos^2 (x) - sin^2 (x) + sin^2 (x) + cos^2 (x)) / cosx = 10cos^2 (x) / cos (x) = 10cos (x)

Б) y' = (ctgx/tgx) ' = ((ctg (x) '*tgx-ctgx * (tgx) ') / (tgx) ^2 = (-1/sin^2 (x) * tgx - ctgx * (1/cos^2 (x))) / (tgx) ^2 = (-1 / (sinx*cosx) - 1/

(sinx*cosx)) / (sinx/cosx) ^2=-2 / (sinx*cosx) * (cosx/sinx) ^2=-2cosx / (sin (x) ^3

2) Y' = (sin (x^5-8x^3+5x)) ' = (x^5-8x^3+5x) '*cos (x^5-8x^3+5x) = (5x^4-24x^2+5) * cos (x^5-8x^3+5x)