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Question 11:
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,
