Please show all steps before get to the answers.
1. Differentiate (3x^2− 5)^3.
2. Find dy/dx if y = sqrt (x^2 + 1).
3. The daily profit, P, of an oil refinery is given by
P = 8x − 0.02×2,
where x is the number of barrels of oil refined. How many barrels will give maximum profit and what is the maximum profit?
4. ∫ 2cos(w)−sec(w)*tan(w) dw
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