MULTIPLE CHOICE THE DERIVATIVE OF A FUNCTION
Question 1. What's the definition of derivative?
A. lim
𝑓(𝑥+Δ𝑥)−𝑓(𝑥0 )
∆𝑥→0
Δ𝑥
.
B. lim
𝑓(𝑥)−𝑓(𝑥0 )
𝑥→0
𝑥−𝑥0
C. lim
𝑓(𝑥)−𝑓(𝑥0 )
𝑥→𝑥0
D. lim
𝑥−𝑥0
𝑓(𝑥0 +Δ𝑥)−𝑓(𝑥)
∆𝑥→0
Δ𝑥
.
Question 2. If the position function for a particle is 𝑠(𝑡 ) = −𝑡 2 − 𝑡, what is the instantaneous velocity
function for the particle?
A. v(t) = -2
C. v(t) = t3
B. v(t) = -2t – 1
D. v(t) = -t
Question 3. If the position of a particle is represented by s(t) = -t2 + 1, what is its instantaneous
velocity at t = 1?
A. Velocity = 0
B. Velocity = 1
C. Velocity = -1
D. Velocity = -2
Question 4. Find the derivative of f(x) = 5x2 + 7x - 3.
A. 2x + 7
B. 10x + 7
C. 10x + 4
D. 2x + 4
C. 12
D. 2x
Question 5. Find 𝑓′(2) if 𝑓 (𝑥) = 𝑥 2 + 2𝑥
A. 2x + 2
B. 6
Question 6. Find the slope of the tangent line to f(x) = -3x2- 6x at x = 1.
A. m = 0
B. f'(x) = -6x – 6
C. f'(x) = 6x
D. m = -12
Question 7. Find the derivative of f(x)=(x5 +3).4x3
A. 4x8+60x6+12x3
B. 12x7+36x2 C. 32x7+36x2 D. 20x6
Question 8. Find the derivative of 𝑓 (𝑥) =
A. 𝑓 ′ (𝑥) =
C. 𝑓 ′ (𝑥) =
5𝑥 3 +1
2𝑥−3
(2𝑥−3).15𝑥 2 −(5𝑥 3 +1).2
B. 𝑓 ′ (𝑥) =
(5𝑥 3 +1)2
(5𝑥 3 +1).2−(2𝑥−3).15𝑥 2
D. 𝑓 ′ (𝑥) =
(5𝑥 3 +1)2
(2𝑥−3).15𝑥 2 −(5𝑥 3 +1).2
(2𝑥−3)2
(5𝑥 3 +1).2−(2𝑥−3).15𝑥 2
(2𝑥−3)2
Question 9. Find the derivative of y = (x2 + 1)3
A. y’ = 3(x2 + 1)2
B. y’ = 3(2x)2
C. y’ = 3(x2 + 1)2(2x)
Question 10. Find the derivative of 𝑓(𝑥) =
6
A. 𝑓 ′ (𝑥) = 𝑥 −5
B. 𝑓 ′ (𝑥) = − 5
D. y’ = 2x(x2 + 1)2
−5
5
√𝑥
1
√𝑥 6
C. 𝑓 ′ (𝑥) =
1
5
√𝑥 4
D. 𝑓 ′ (𝑥) = 𝑥
Question 11. Find the derivative of f(x) = sin(cos(2x-5))
A. -2(sin2(2x-5))
B. -2cos(cos(2x-5))(sin(2x-5))
C. -(cos(2x-5))(sin(2x-5)
D. 2sinxcos(2x-5)
Question 12. Find the derivative of f(x) = cos(5x4)
A. f'(x) = sin(20x3)
B. f'(x) = 20x3 sin(5x4)
C. f'(x) = -sin(20x3)
D. f'(x) = -20x3 sin(5x4)
Question 13. Find the derivative of f(x) = x2 + ex - cosx
A. f’(x) = 2 + ex + cosx
B. f’(x) = 2 + xex + cosx
C. f’(x) = 2x + ex – cosx
D. f’(x) = 2x + ex + sinx
Question 14. Find the derivative of y=5x2e3x
A. y' = 10xe3x(2x+3)
B. y' = 5xe3x(3x+2)
C. y' = 10ex3x(3x+2)
D. y' = 5xe3x(2x+3)
Written by Minh Thien Nguyen.