MATH 1350 Midterm: Math135SampleExam2Solutions
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Math 135 - spring 2008 - instructor: dr. radu c. cascaval: find the derivatives of the following functions. Simplify when possible. (a) f (x) = sin 3x. 2x (d) x = t(2t 3) (b) g(x) = (x + 1)2(x2 + 2) (e) r = cos (c) y = ln(x 1) (f) y = sin3(ln(2x 1)) 2x2 (b) g (x) = 2(x + 1)(2x2 + x + 2) (c) y = (d) dx dt. 2x 1: find the equation of the tangent line to the curve at the indicated point y = xe1 2x at x = 1. = 3 sin2(ln(2x 1)) cos(ln(2x 1)) Horizontal tangent at x = 1 y = 1. 2: (a) find the derivative of the following function f (x) = X 1 x2+1 . (b) find the points where the graph y = f (x) has horizontal tangents. One value is extraneous (since only x > 1 is allowed).
