a.maths問題....20分!!!

We should use quotient rule.

y = x / cosx

dy/dx = [cosx(dx/dx) - xd(cosx)/dx] / cos2x

= (cosx - x(-sinx)) / cos2x

= (cosx + xsinx) / cos2x

d2y/dx2 = {cos2x d/dx (cosx + xsinx) - (cosx + xsinx) d(cos2x)/dx} / (cos2x)2

= [cos2x(-sinx + sinx + xcosx) - (cosx + xsinx)(-2sinxcosx)] / cos4x

= (xcos3x + 2sinxcos2x + 2xsin2xcosx) / cos4x

= (xcos2x + 2sinxcosx + 2xsin2x) / cos3x

= (x + xsin2x + sin2x) / cos3x