Math 1271, Summer 2010, Worksheet 13.11. Starting with the identity sin2x + cos2x = 1, prove that tan2x + 1 = sec2x.2. Starting with the identity cos(x + y) = cos x cos y − sin x sin y, prove that cos(2x) =cos2x − sin2x.3. Let f(x) = (5 + g(x2))32. Suppose that g(3) = −4, g(6) = 10, g(9) = 11, g0(3) = 9,g0(6) = 3, and g0(9) = 5. Find f0(3).4. Below is a graph of the equation y3−3y2−24y −5x + 30 = 0. How many functions aredefined by this equation for −30 ≤ x ≤ 20? The values of y corresponding to x = −425arey = 3, y =√24 and y = −√24. Finddydxat these three points.-40-2002040-10-505101Math 1271, Summer 2010, Worksheet 13.21. Let f(x) = ln(x4) and g(x) = (ln x)4. Find f0(x) and g0(x).2. Let f(x) = x3ln x. Find f00(x).3. Let f(x) = ln((3x + 5)√x2+ 4). First simplify the log and then find f0(x).4. Let y = lnq5x2+83x−2. First simplify the log and then finddydx.5. Let f(x) = sin(x4) and g(x) = (sin x)4. Find f0(x) and g0(x).6. Let f(x) = arcsin(x2+ 1). Find f0(x).7. Let g(x) =√1 − x2arcsin x for |x| ≤ 1. Find g0(x) and
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