Math203-Midterm-Winter-2012

3 4 let f x continued on the other side 1 1 12

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Unformatted text preview: t f (x) = (continued on the other side) 1 1 [12] 5. Find the derivatives of the following functions (you don’ need to simplify the …nal answer, but you must show how t you calculate it): (a) f (x) = 3x2=3 1 + x3 (b) f (x) = ex (sin x cos x) q p (c) f (x) = x + x2 + 1 (d) f (x) = ln(1 + arctan x) 1 . x (a) Use the de…nition of derivative [6] 6. Let f (x) = f (x+h) f (x) h h!0 f 0 (x) = lim to …nd f 0 (2). (b) Find the equation of the tangent line T (x) to the graph of f (x) at the point (2; f (2)). [3] Bonus Question. Use the de…nition jxj = p x2 and the Chain Rule to show that if f (x) = j sin xj sin x cos x whenever sin x 6= 0. j sin xj What can you say about f 0 (x) when sin x = 0 ? then f 0 (x) = 2...
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