MATH 205 Quiz: MATH 205 Louisville Quiz 4 111021 Solutions
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Quiz #4 solutions: (12 points) compute the following derivatives: (a) (4 points) given y = x2esec x, nd dy dx . This is a product rule stacked with a chain rule (since esec x is a composition). Let us pre- emptively assign u = sec x, so that dy dx d eu dx x2(cid:19) esec x + x2 d dx(cid:0)x2esec x(cid:1) = 2xesec x + x2(sec x tan x)eu. = 2xesec x + x2 sec x tan xesec x du dx eu d (b) (4 points) for f (t) = cos(cid:16) et arcsin t(cid:17), nd f (t). This is a chain rule problem whose internal calculation is itself a quotient rule. 2 cos(cid:18) et arcsin t(cid:19) cos u f (t) = d dt d dt du dt cos u d du et du dt. 1 t2 (cid:18) sin ( sin u) arcsin t(cid:19) 2 et (c) (4 points) compute d d sin ( + ln ).
