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Question
Differentiate the following with respect to x.
cos2 x
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Solution
For the following problems chain rule to be used:
`"d"/"dx"` f(g(x)) = f'(g(x)) . g'(x)
`"d"/"dx"` [f(x)]n = n[f(x)]n-1 × `"d"/"dx"`f(x)
y = cos2 x = (cos x)2
`"dy"/"dx" = 2 (cos x)^(2 - 1) "d"/"dx" (cos x)`
= 2 cos x (-sin x)
= -2 sin x cos x
= -sin 2x
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