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Question
Differentiate the following with respect to x.
cos3 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 = cos3 x
y = (cos x)3
`"dy"/"dx" = 3(cos x)^(3-1) "d"/"dx" (cos x)`
= 3 cos2 x (-sin x)
= -3 cos2 x sin x
= -3 cos x (sin x cos x) [Multiply and divide by 2]
= `(-3)/2` cos x (2 sin x cos x)
= `(-3)/2` cos x sin 2x
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