Question 8 of 71intermediate🔧 ApplyShort Answer7 marks

Find the derivative of the following functions:

(i)

sinxcosx\sin x \cos x

Answer

cos 2x

(ii)

secx\sec x

Answer

sec x tan x

(iii)

5secx+4cosx5\sec x + 4\cos x

Answer

5 sec x tan x - 4 sin x

(iv)

cosecx\cosec x

Answer

-cosec x cot x

(v)

3cotx+5cosecx3\cot x + 5\cosec x

Answer

-3 cosec²x - 5 cosec x cot x

(vi)

5sinx6cosx+75\sin x - 6\cos x + 7

Answer

5 cos x + 6 sin x

(vii)

2tanx7secx2\tan x - 7\sec x

Answer

2 sec²x - 7 sec x tan x

Explanation

This question tests application of derivative rules for trigonometric functions. Students must apply the product rule for part (i), quotient rule for parts (ii) and (iv), and sum/difference rules for remaining parts. The context provides key derivatives: d/dx(tan x) = sec²x and d/dx(cot x) = -cosec²x, along with product and quotient rule formulas.