Posted by ct on Thursday, December 22, 2011 at 7:19pm.
I will assume you meant
y = tan (x^2) / (1 + cosx)
by quotient rule,
dy/dx = ( (1+cosx)(sec^2 (x^2))(2x) - tan x^2 (-sinx) )/(1+cosx)^2
I don't know what level of simplification you need
y = e^(x^3) - tan 6x
dy/dx = (3x^2)e^(x^3) - 6 sec^2 (6x)