Review on Derivatives & Integrals Before Calc II
(Q1.) (a) d (sin3 x)
dx
(Q2.) (a) d (tan−1( x ))
dx
1
(Q3.) (a) d (e x )
dx
4⎞
⎛
(Q4.) (a) d ⎜⎜1+ 2x ⎟⎟⎟
dx ⎝ x ⎠
(Q5.) (a) d ln x + x 2 + 1
dx
cosx
(Q6.) (a) ⌠
⌡ 1+ sin2 x dx
(Q7.) (a) ∫ tan(2 x )sec(2 x ) dx
(b) d (sin(x 3))
dx
(b) d xtan−1x − 1 ln(1+ x 2 )
dx
2
(b) d 1x
dx e
⎛ 2 ⎞
(b) d ⎜⎜ x 4 ⎟⎟⎟
dx ⎝1+ x ⎠
(b) d ln x x 2 + 1
dx
cosx
(b) ⌠
⌡ 1+ sinx dx
(Q8.) (a) ⌠ 1 x dx
⌡ e
(Q9.) (a) ⌠ 1 dx
⌡ 1− x
(b) ⌠ x1 dx
⌡ e −1
1
(b) ⌠
dx
⌡ x + 1− x
((
(Q10.) (a)
))
∫ sin x sec x dx
2
( )
(Q11.) (a) d 3 x 2
dx
(Q12.) (a) d (tanx)
dx
(Q13.) (a) d ((2 x + 3)5)
dx
(Q14.) (a) d (π x )
dx
⎛
⎞
(Q15.) (a) d ⎜⎜ 1 x ⎟⎟⎟
dx ⎝⎜ e ⎠⎟
( )
(Q16.) (a) d lnx
dx x
(Q17.) (a) d x x 2 + 1
dx
(Q18.) (a) d (sin2x cosx)
dx
⎛
⎞
(Q19.) (a) d ⎜⎜ 1 2 ⎟⎟⎟
dx ⎜⎝ 1− x ⎟⎠
(
⎛ x ⎞
(Q20.) (a) d ⎜⎜ e 2 x ⎟⎟⎟
dx ⎝1+ e ⎠
)
(
)
( )
((
(b)
(b)
))
∫ tan x sec x dx
2
2
∫ tan x sec x dx
2
∫ x dx
(b) ∫ tanx dx
(b) ∫ (2 x + 3)
(b) ∫ π dx
(b)
2
3
5
dx
x
(b) ⌠ 1 x dx
⌡ e
(b) ∫ lnx dx
x
∫ x x + 1 dx
(b) ∫ sin x cosx dx
2
(b)
2
(b) ⌠ 1 2 dx
⌡ 1− x
x
(b) ⌠ e 2 x dx
⌡ 1+ e
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