求y=(x+cosx)/(x+sinx)的导数

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求y=(x+cosx)/(x+sinx)的导数

求y=(x+cosx)/(x+sinx)的导数
求y=(x+cosx)/(x+sinx)的导数

求y=(x+cosx)/(x+sinx)的导数
y'=[(1-sinx)(x+sinx)-(1+cosx)(x+cosx)]/(x+sinx)²=[sinx-cosx-xsinx-xcosx-1]/(x+sinx)²

(sinx - xsinx - cosx - xcosx - 1)/(x sinx)^2 (1)y`=10x-4 (2)y`=4x(3x^2 1) (2x^2-1)(6x) =12x^3 4x 12x^3-6x =

y = 1 + (cosx-sinx)/(x+sinx)
y ' = [(-sinx-cosx)(x+sinx) - (cosx - sinx)(1+cosx) ]/(x+sinx)^2
= ( x sinx + x cosx + sinx - cosx -1) / (x+sinx)^2