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Question
sin3x cos3x
Solution
`d/(dx) (sin^3x cos^3x) = sin^3x * d/(dx) cos^3x + cos^3x * d/(dx) (sin^3x)`
= `sin^3x * 3 cos^3x (- sin x) + cos^3x * 3 sin^2x * cos x`
= `-3 sin^4x cos^2x + 3 cos^4x sin^2x`
= `3 sin^2x cos^2x (- sin^2x + cos^2x)`
= `3 sin^2x cos^2x * cos 2x`
= `3/4 4 sin^2x cos^2x * cos 2x`
= `3/4 (2 sin x cos x)^2 cos 2x`
= `3/4 sin^2 2x * cos 2x`
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