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Question
Differentiate the following with respect to x.
sin x cos x
Solution
Let y = sin x cos x
`"dy"/"dx" = sin x "d"/"dx" (cos x) + cos x "d"/"dx" (sin x)`
= sin x (-sin x) + cos x cos x
= -sin2 x + cos2 x
= cos2 x – sin2 x
= cos 2x [∵ cos 2x = cos2 x – sin2 x]
(or) y = sin x cos x
y = `1/2` (2 sin x cos x)
y = `1/2` sin 2x
`"dy"/"dx" = 1/2` cos 2x . 2 = cos 2x
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