Here are the formulas you should remember about derivation:

cos(x)' = -sin(x)

cos(u)' = -sin(u)(du/dx)

sin(x)' = cos(x)

sin(u)' = cos(u)(du/dx)

tan(x)' = sec2(x)

tan(u)' = sec2(u)(du/dx)

cot(x)' = -csc2(x)

cot(u)' = -csc2(u)(du/dx)

sec(x)' = sec(x)tan(x)

sec(u)' = sec(u)tan(u)(du/dx)

csc(x) = -csc(x)cot(x)

csc(u) = (-csc(u)cot(u))(du/dx)