APPM 1345 Midterm: appm134spring2013exam3_sol
Document Summary
Spring 2013 (b) solution 1: use logarithmic differentiation: (12 points) match the graphs shown to the following functions. No explanation is necessary. (a) y = ex (b) y = e x (c) y = ln x (d) y = 4x (e) y = 4 x (f) y = log4 x y. Solution: (a) 4 (b) 1 (c) 5 (d) 3 (e) 2 (f ) 6: (18 points) find dy/dx for each of the following equations. (a) y = 5ln x. X (b) y = x (c) sec(xy) = ln(cos x) Solution: (a) y = 5ln x y = 5ln x(ln 5) Solution 2: express x as eln x. ( x ln x) y = x. 2 x(cid:19) (c) sec(xy) = ln(cos x) sec(xy) tan(xy)(xy + y) = sec(xy) tan(xy)(xy + y) = tan x cos x ( sin x) Tan x sec(xy) tan(xy) y y = Tan x x sec(xy) tan(xy) y x cos x.
