Question: Let f(x) = tan x = sin x cos x on ( / 2 , / 2 ). Note that f is continuous. (a) Sketch

Let f(x) = tan x = sin x cos x on ( / 2 , / 2 ). Note that f is continuous. (a) Sketch the graph of f. (b) Find f ' (x). (c) Explain why f is strictly increasing. So f has an inverse function, f ^1 (x) = arctan x. (d) Sketch the graph of arctan x. (e) Find the derivative of arctan x.

P.s. I don't think I can revise the wording. I don;t know how to do these problems! I am not going just copy answers because there will not be anyone during exams!! Thanks!!

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