(1) sin(2x + 1)

APPLIED CALCULUS I – MATH. 215
Differentiation Problems
Differentiate the following functions:
(1) sin(2x + 1) (2) tan(3x2 − 2) (3) cos(1/(x + 1)) (4) 4 sin(1 + cos x) (5) sin(x2 ) cos(3x)
p
(6) (3x2 + 2)5 (7) csc(3x − 1) (8) 5x3 − 2 (9) (x3 − 8)4/3 (10) (x2 + sin x)2 (11) (1 + cos x)1/4
p
p
(12) sin((x + 1)/(x − 1)) (13) (x2 − 1)/(x + 3) (14) (1 − sin x)/(3 + cos x) (15) sec5 (3x2 − 5)
p
p
(16) [(1 − sin x)/(3 + cos x)]3/4 (17) 1 + 3 tan(2x) (18) 6x2 − 5 (19) (2 + 5x2 )1/4 (20) sin5 (x2 )
(21) tan2 (3x + 5) (22) (2 + 5x2 )1/4
(23) sin(x2 cos x)
(24) (x + 4)7
(25) (x2 − 4)−2/3
(27) sec(1/x) (28) sec3 (1/x2 ) (29) tan(1/(1 + x2 )) (30) sin(2 − cos x)
(32) tan(1 + sin x) (33) (1 + sin x)3
(34) (1 − 2x3 )−5/6
(26) sec(x3 )
(31) sin2 (2 + tan x)
(35) tan1/4 (x − 2) (36) sin−2/3 (x2 + 1)
(37) sin(2 − cos2 x) (38) sin2 (2 + cos x)
(42) x2 cos x2
(39) x tan(x2 − 1) (40) tan[x sin2 (x + 2)] (41) x2 cos2 x
√
(43) x2 cos(x3 − 5) (44) x sin x (45) x/(1 + cos2 x) (46) (1 + cos2 x)/x
(47) sec(1/(1 + sin x))
(48) (tan x)(cot x2 ) (49) (tan x)(cot2 x2 ) (50) 2x(x3 − 5)7
(51) sec7 (sin x)
(52) (tan x)(sec x2 ) (53) (x2 − 1)5 sin2 x
(57) (sin x)/(1 + x2 )
(58) (1 − x6 )−3/4
(54) x tan x (55) (tan x)/x (56) (x − 1)2/3 sin x
p
(59) (1 − x)/(1 + x5 ) (60) x2 (1 + x2 )1/7 (61) csc(1/x2 )
(62) sec3/4 (1 − x2 ) (63) sec−1/4 (1 + x) (64) (4 + sin x)−6/7 (65) 1/(2 + cos(x2 + 5)) (66) sin(tan x)
√
(67) tan x + sec x (68) (tan x + cos x)−1/3 (69) tan[(x + 2)/(x − 1)] (70) sin[(x2 − 1)/(x2 + 1)]
(71) x cos(x2 + 1) (72) (x2 + 1) csc2 (x2 + 1) (73) (sin2 x)/(x3 + 5x2 − 4x + 1) (74) (sec2 x)/x2
(75) sin(tan x) (76) tan(sin x) (77) (1 + tan x)−2/3 (78) (1 + 3 sin x)2 (79) (1 + sin(3x))2
√
(80) x cos x (81) x2/3 sin x (82) x−1/3 tan(x2 ) (83) sin1/2 (x2 + 2x − 1) (84) cos(cos x)
p
(85) cos1/4 (3 + sin(2x)) (86) (x2 − 5)32/17 (87) (x4 + 1)3 + 5 (88) 4 sin2 x − 3 cos x + 17
(89) cos1/3 (cos x)
(90) [1 + cos2 (x + 2)]2 (91) 3 cos5 (x − 3) (92) tan(sec x) (93) (x4 − 5x2 + 2)7
p
√
(94) 8x7 − 4x3 + 1 (95) 2x + 5 (96) sin4 (1/(1 − x)) (97) sin2 x + 5 (98) cos3 (3x2 − 3)
p
(99) 2 + x2 + 1 (100) (5 − cos2 x)1/12