Find the derivative of the following functions:

(i) sin x cos x (ii) sec x (iii) 5 sec x + 4 cos x

(iv) cosec x (v) 3cot x + 5cosec x

(vi) 5sin x – 6cos x + 7 (vii) 2tan x – 7sec x

(i) Let f (x) = sin x cos x. Accordingly, from the first principle,

(ii) Let f (x) = sec x. Accordingly, from the first principle,

(iii) Let f (x) = 5 sec x + 4 cos x. Accordingly, from the first principle,

(iv) Let f (x) = cosec x. Accordingly, from the first principle,

(v) Let f (x) = 3cot x + 5cosec x. Accordingly, from the first principle,

From (1), (2), and (3), we obtain

(vi) Let f (x) = 5sin x – 6cos x + 7. Accordingly, from the first principle,

(vii) Let f (x) = 2 tan x – 7 sec x. Accordingly, from the first principle,