(vii) 2 tan x – 7 sec x

(i) Let f(x) = sinx cos x

Using product rule, we have

f'(x) = sin x

      = sin x (- sin x) + cos x (cosx)

      = - sin²x + cos²x = cos²x – sin²x

(ii) Let f(x) = sec x

f’(x) = = =

      = =

      = = sec x tan x.

(iii) Let f(x) = 5 sec x + 4 cos x

f’(x) =

      =

      = 5

      = 5 sec x tan x – 4 sin x

(iv) Let f(x) = cosec x

f’(x) = = =

      = = = -cosec x cot x

v) Let f(x) = 3 cot x + 5 cosec x

f’(x) =

      =

      =

      = 3

      = 3

      = 3

      = 3

      = -3 cosec²x – 5 cosec x cot x.

(vi) Let f(x) = 5 sinx – 6 cos x + 7

f’(x) =

      =

      = 5 cos x – 6(- sin x) + 0 = 5 cos x + 6 sin x

(vii) Let f(x) = 2(tan x – 7 sec x)

f’(x) =

      =

      = 2

      = 2

      = 2 - 7 sec x tan x

      = 2 sec²x – 7 sec x tan x