Math E-15 Homework 5 1. Find the derivative of each of the following functions. (a) y = sin(7x) (b) y = 2sin(7x) (c) y = cos(2sin(7x) ) (d) y = ln(sin(x3 )) p (e) y = arctan(log10 (5x)) (f) y = e3x tan(2x4 ) (g) y = sin(cos(x 23x )) (h) y = (1 + x6 )8x (i) y = e2 + ln 3 + sin 4 + arctan 5 2 2. Consider the function f (x) = ex . 2 2 [Remember that ex means e(x ) , NOT (ex )2 and that x2 means (x2 ), NOT (x)2 .] Note: Be sure to show enough work on parts (a) and (b) that it is clear to the grader how you used calculus (and not a graphing calculator or someone else's paper) to do the problem. (a) On what interval(s) is f increasing? On what interval(s) is f decreasing? (b) On what interval(s) is f concave up? On what interval(s) is f concave down? (c) Sketch a graph of f , labeling the points you found above