MATH 171 Midterm: Math 171 TAMU Spring 15 Exam3M171Solutions
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All work you wish graded must be in your blue book. Answers must be justi ed; no explanation, no credit: (15) evaluate the following: (a) cos 1(cos (1/2)) (b) sin 1(sin (3 /2)) cos 1(cos (1/2)) = Note that the range of the arcsine function is [ /2, /2]. (c) sin(cid:0)tan 1 x(cid:1) We need to draw a right triangle to get this one. Thus, sin(cid:0)tan 1 x(cid:1) = sin = x. 1 + x2: (20) calculate the derivatives of the following functions. Do not simplify. (a) 2x (b) log6 x (c) sin 1(cid:0)x2 + 1(cid:1) (d) cos(cid:0)tan 1(4x)(cid:1) d dx. 2x = d dx ex ln 2 = (ln 2) ex ln 2 = (ln 2) 2x . d dx log6 x = d dx (cid:18) ln x ln 6(cid:19) = It"s easier to determine the value of cos(cid:0)tan 1(4x)(cid:1) rst. Thus, d dx (cid:0)cos(cid:0)tan 1(4x)(cid:1)(cid:1) = dx (cid:0)1 + 16x2(cid:1) 1/2.
