(a) Differentiate the equation θ = 9t² – 2t³ with respect to t.
(b) Differentiate the equation y = 3 sin 5t with respect to t.
(c) Differentiate the equation y = 2e6t with respect to t.
(d) Determine ∫▒〖x^7 dx〗.
(e) Determine ∫ (5sin 3t – e3t) dt.
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