Find the derivative of the following functions:

Question 41 of 70intermediate🔧 ApplyShort Answer7 marks

(i)

$\sin x \cos x$

Answer

cos 2x

(ii)

$\sec x$

Answer

sec x tan x

(iii)

$5\sec x + 4\cos x$

Answer

5 sec x tan x - 4 sin x

(iv)

$\cosec x$

Answer

-cosec x cot x

(v)

$3\cot x + 5\cosec x$

Answer

-3 cosec²x - 5 cosec x cot x

(vi)

$5\sin x - 6\cos x + 7$

Answer

5 cos x + 6 sin x

(vii)

$2\tan x - 7\sec x$

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.

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