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Differentiate with respect to theta

  • Calculus -

    y = (sin3θ tan3θ)^12
    y' = 12(sin3θ tan3θ)^11 (3cos3θtan3θ + 3sin3θsec^2 3θ)
    = 108(sin3θtan3θ)^11(sin3θ+sin3θ(1+tan^2 3θ))
    = 108(sin3θtan3θ)^11 (2sin3θ + sin3θtan^2 3θ)

    or other ways

    or, expanding first,

    y = sin^12 3θ * tan^12 3θ
    y' = 12sin^11 3θ tan^12 3θ (3cos 3θ) + 12sin^12 3θ tan^11 3θ (3sec^2 3θ)

    which I'm sure massages out to the same.

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