Quiz about Calculus

Question 1

FInd the derivative:

f(x) = (-2/3)x³ - (1/2)x² + 9x

Accepted Answer

-2x² - x + 9

Answer

-2x² + x + 9

Answer

2x² - x + 9

Answer

2x² - x - 9

Question 2

Find the second derivative of the function:
f (x) = 2x - 5x⁶

Accepted Answer

f ''(x) = -150x⁴

Answer

f ''(x)= 2 - 30x

Answer

f ''(x) = 2-30x⁵

Answer

f ''(x) = -30x⁵

Question 3

Set up the derivative of y=(3x⁴- 7)*(5x²+ 1)

Accepted Answer

(3x⁴ - 7)*(10x) + (12x³)*(5x² + 1)

Answer

(12x³)*(10x)

Answer

(3x⁴ - 7)*(10x) - (12x³)*(5x² + 1)

Answer

(3x⁴ - 7)/(10x) + (12x³)/(5x² + 1)

Question 4

Find the derivative of y = 2x² (3x - 4)

Accepted Answer

18x² - 16x

Answer

6x³ - 8x²

Answer

15x2 - 6x

Answer

6x - 4

Question 5

Differentiate f(x) =(2/ x⁵) - 5.

Accepted Answer

-10x-6

Answer

x5-3

Answer

-10x6

Answer

x5-5

Question 6

Find the derivative of the given equation
f(x) = x⁴ + 4x³- 2x²

Accepted Answer

4x³ + 12x²- 4x

Answer

x³ + x²- x

Answer

4x³ + 12x²+ 4x

Answer

4x + 12x - 4x

Question 7

Find the derivative.

Accepted Answer

x⁴cosx + 4x³sinx

Answer

x⁴cosx - 4x³sinx

Answer

4x3cosx

Answer

-4x3cosx

Question 8

Find the derivative f(x) = xe^x

Accepted Answer

f'(x) = e^x + xe^x

Answer

f'(x) = e^x

Answer

f'(x) = xe^x + xe^x

Answer

f'(x) = e^x - xe^x

Question 9

.

Accepted Answer

(3x²-2)cos(x³-2x)

Answer

-(3x²-2)cos(x³-2x)

Answer

cos(2x²-2)

Answer

sin(2x²-2)

Question 10

Find the derivative of g(x)=(3x-2)/(x²+2)

Accepted Answer

(-3x²+4x +6)/(x²+2)²

Answer

9x2+2

Answer

3(x²+2)/(x²+2)²

Answer

(-3x²+10)/(x²+2)²

Question 11

The position of an object is given as a function of time by x = 3t² + 5t³- 2t
What is the acceleration of the object at time t = 2 s?

Accepted Answer

66 m/s/s

Answer

64 m/s/s

Answer

60 m/s/s

Answer

70 m/s/s

Question 12

The velocity of an object is given as v = 2t + 3t³. what is the acceleration of the object at t = 2 s?

Accepted Answer

38 m/s/s

Answer

27 m/s/s

Answer

16 m/s/s

Answer

49 m/s/s

Question 13

If the position function for a particle is s(t) = -t² - t, what is the instantaneous velocity function for the particle?

Accepted Answer

v(t) = -2t - 1

Answer

v(t) = -2

Answer

v(t) = t3

Answer

v(t) = -t

Question 14

If the position of a particle is represented by x(t) = -t² + 1, what is its instantaneous velocity at t = 1?

Accepted Answer

v = -2

Answer

v = 0

Answer

v = 1

Answer

v = -1

Question 15

Find the derivative.
f(x) = -8x^-3 + 5x - e^x

Accepted Answer

f'(x) = 24x^-4 + 5 - e^x

Answer

f'(x) = -24x^-4 + 5 - e^x

Answer

f'(x) = 24x^-2 + 5 - e^x

Answer

f'(x) = 24x^-4 + 5 - e^x-1

Question 16

Find the derivative
f(t) = (t² + 2t)⁵

Accepted Answer

f'(t) = 5(t² + 2t)⁴(2t + 2)

Answer

f'(t) = 5(2t+2)⁴

Answer

f'(t) = 5(t² + 2t)⁴

Answer

f'(t) = 5(t² + 2t)⁴(2t)

Question 17

Find the second derivative of
f(x) = x²+ e^x - cosx

Accepted Answer

f"(x) = 2 + e^x + cosx

Answer

f"(x) = 2x + e^x + cosx

Answer

f"(x) = 2x + xe^x - cosx

Answer

f"(x) = 2x + e^x + sinx

Calculus

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