my derivative quiz (calculus 1)

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The Derivative Quiz
Your name:
(Q1.) If y = sin( x 2 + y 2 ) , then
(A)
2 x cos( x 2 + y 2 )
1−2 y cos( x 2 + y 2 )
Date
dy
=?
dx
y = sin( x 2 + y 2 )
2 x sin( x 2 + y 2 )
(B)
1−2 y sin( x 2 + y 2 )
2 x sin( x 2 + y 2 )
(C)
1+ 2 y cos( x 2 + y 2 )
(D) 2 x sin( x 2 + y 2 )+ 2 y sin( x 2 + y 2 )
(E) 2 x cos( x 2 + y 2 )+ 2 y cos( x 2 + y 2 )
(Q2.)
d ⎛⎜ e x ⎞⎟
⎟= ?
⎜
dx ⎜⎝ 1+ x ⎟⎠
x +ex
(A)
(1+ x )2
xe x
(B)
(1+ x )2
2 xe x
(C)
(1+ x )2
1+ e x
(D)
(1+ x )2
−e x
(E)
(1+ x )2
1
(Q3.) If f ( x ) = e
(A) e
(B) e
(C) e
(D)
1+ 2 x
, then f ′(x ) = ?
1
1+ 2 x
2
1+ 2 x
1
2 1+ 2 x
e
1+ 2 x
2 1+ 2 x
e 1+ 2x
(E)
1+ 2 x
(Q4.) If y = tan−1(2 x + 1) , then f ′(x ) = ?
1
(A)
2
2x + 1
1
(B)
2
4x + 2
2
(C)
2x + 1
1
(D)
2
2x + 2x + 1
1
(E)
2
4x + 4x + 2
(Q5.)
d
(sec 4 x ) = ?
dx
(A) 4sec 4 x tan x
(B) 4sec3 x tan3 x
(C) 4 tan3 x sec x
(D) 4sec3 x +sec x tan x
(E) 4 tan3x + sec2 x
2
(Q6.)
d2
cos−1 x ) = ?
2(
dx
x
(A)
(1− x 2 )3
(B)
−x
(1− x 2 )3
(C)
x
2 (1− x 2 )3
−1
sin2 x
1
(E)
cos2 x
(D)
(Q7.) Find the second derivative of f ( x ) = sin( x 3 )
(A) f ′′( x ) = 6 x cos( x 3 )−9 x 4sin( x 3 )
(B) f ′′( x ) = 6 x sin( x 3 )−9 x 4 cos( x 3 )
(C) f ′′( x ) = −6 x sin( x 3 )+ 9 x 4 cos( x 3 )
(D) f ′′( x ) = −3 x 2 sin( x 3 )
2
(E) f ′′( x ) = −sin(3 x )
(Q8.) Find y ′ if y = x 2 (1+ 3 x 4 )
(A) 1+ 23 x 4
(B) 2 x + 24 x 7
(C) 3 x + 12 x 4
(D) 2 x + 18 x 5
(E) 24 x 4
3
⎛ x ⎞⎟
(Q9.) Differentiate f ( x ) = ln⎜⎜
⎟
⎜⎝ 1+ x 2 ⎟⎟⎠
1−3 x 2
(A)
2 x (1+ x 2 )
1+ 3 x 2
(B)
2 x (1+ x 2 )2
1−3 x 2
(C)
2 x (1+ x 2 )
3x 2
(D)
2
x (1+ x 2 )
(E)
1−3 x 2
2
2 x (1+ x 2 )
d ⎛⎜ x ⎞⎟
⎟= ?,
⎜
dx ⎜⎝ 1+ x 2 ⎟⎟⎠
1−3 x 2
(A)
2
x (1+ x 2 )
(Q10.)
1−3 x 2
2 x (1+ x 2 )
1−3 x 2
(C)
2
2 x (1+ x 2 )
(B)
(D)
1−2 x 2
2 x (1+ x 4 )
(E)
−2 x 2
2
2 x (1+ x 2 )
End of quiz. Your score is __________
4