Problems to practice-derivatives|||{ Calculus I Find derivatives of the following functions: (1)y = 2 + 3×2; (2)y = 1x ; (3)y = 1x + a (4)y = 1 x2 + a2 (5) y = apx (6) y = px2 + a2 =============== Answers: 6x;?? 1 x2 ;?? 1 x2 ; ??2 x3 ; a 2px ; p x x2+a2 ================ (7)y = x2 sin x (8)y = x3ex (9)y = x3 ln x (10)y=x3 tan x (11)y = ln sin x ============== Answers: x2(3 sin x + x cos x); (3 + x)x2ex; x2(3 ln x + 1); x2(3 tan x + x sec2 x); x2(3ln(sin x) + x cot x) ============== (12)y = x4= sin x (13)y = sin x=x4 (14)y = sin x=ex (15)y = ex= sin x 1
==================== Answers: x3(4 ?? x cot x) csc x; (x cos x ?? 4 sin x)=x5; (cos x ?? sin x)=ex; ex(cos x ?? sin x) csc2 x ==================== (16)y = 2px sin x (17)y = 3 tan x=px (18)y = (5 + 4ex)=px (19)y = ex(x3 + px) (20)y = (x3 + x4)(ex ln x) ====================== Answers: (sin x + 2x cos x)=px; 3(2x sec2 x ?? tan x)=2×32 ; 2ex(2x ?? 1)=x32 ; ex(2×72 + 6×52 + 2x+)=2×12 ; ex ln x(x4 + 5×3 + 3×2) + ex(x3 + x2) ====================== (21)y = e3x (22)y = e??x (23)y = sin3 x (24)y = psin x (25)y = pln x (26)y = ptan x (27)y = sinpx ======================= Answers: 3e3x;??e??x; 3 sin2 x cos x; cos x=2psin x; 1 2x ln x ; sec2 x 2ptan x ; cospx 2px ======================= (28)y = esin x 2
(29)y = etan x (30)y = ex3 (31)y = epx (32)y = eln x ======================== Answers:esin x cos x; etan x sec2 x; 3x2ex3 ; epx 2px ; 1 ======================== (33)y = ln sin x (34)y = ln tan x (35)y = lnpx (36)y = ln x3 (37)y = sin ln x (38)y = tan ln x (39)y = psin ln x (40)y = psinpx (41)y = ln sinpx (42)y = lnpsinpex (43)y = tan(ln(sin epx)) ============================ Answers:cot x; 2 csc 2x; 1 2x ; 3x cos ln x x ; sec2 ln x x ; cos ln x 2xpsin ln x ; cospx 4pxpsinpx ; cotpx 2px ; pex 4 cotpex; 1 2pxepx cot(epx) sec2 (ln(sin epx)) 3