Quiz about Derivatives Practice

Question 1

Find the derivative of f(x) = 5x² + 7x - 3.

Accepted Answer

10x + 7

Answer

2x + 7

Answer

10x + 4

Answer

2x + 4

Question 2

Question 2.

Accepted Answer

4x⁹ + 6x⁷

Answer

(2/5)x⁹ + (3/4)x⁷

Answer

20x⁹ + 24x⁷

Answer

x⁹ + x⁷

Question 3

Differentiate y = -19

Accepted Answer

0

Answer

-19

Answer

19

Answer

Not differentiable

Question 4

Differetiate y = -19x

Accepted Answer

-19

Answer

0

Answer

19

Answer

Not differentiable

Question 5

Question 5.

Accepted Answer

-32x-9

Answer

(1/2)x-7

Answer

(1/2)x-9

Answer

-32x-7

Question 6

Find the derivative:
y = (4x - 5)(2x + 3)

Accepted Answer

16x + 2

Answer

8

Answer

8x

Answer

16x

Question 7

What is the derivative of sin(x)?

Accepted Answer

cos(x)

Answer

sin(x)

Answer

-sin(x)

Answer

-cos(x)

Question 8

Find f '(2) if
f(x) = x² + 2x

Accepted Answer

6

Answer

2x + 2

Answer

12

Answer

2x

Question 9

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

Accepted Answer

4x³ + 12x²- 4x

Answer

x³ + x²- x

Answer

4x³ + 12x²+ 4x

Answer

4x + 12x - 4x

Question 10

Find dy/dx for
y = (x² + 1)³

Accepted Answer

dy/dx = 3(x² + 1)²(2x)

Answer

dy/dx = 3(x² + 1)²

Answer

dy/dx = 3(2x)²

Answer

dy/dx = 2x(x² + 1)²

Question 11

d/dx (sin²x) = ?

Accepted Answer

2(sin x)(cos x)

Answer

2sin x

Answer

2cos x

Answer

2x(cos x)

Question 12

Find the derivative of f(x)=(x³-2x)²

Accepted Answer

6x⁵ - 16x³+8x

Answer

6x⁵ - 12x³+8x

Answer

x⁶-4x⁴+4x²

Answer

6x⁵ - 16x^3-8x

Question 13

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 14

Question 14.

Accepted Answer

Option A is correct

Answer

B.

Answer

C.

Answer

D.

Question 15

Question 15.

Accepted Answer

Option A is correct

Answer

B.

Answer

C.

Answer

D.

Question 16

What is the limit?

Accepted Answer

17/3

Answer

5/2

Answer

-2/3

Answer

Infinity

Question 17

f' is given, which could be f?

Accepted Answer

C

Answer

A

Answer

B

Question 18

Where is the graph neither continuous nor differentiable?

Accepted Answer

x = -1, 0, 1

Answer

x = -1, 0, 1, 2

Answer

x = -1, 1

Answer

x = -1, 0, 2

Question 19

At which x-value is f continuous but not differentiable?

Accepted Answer

a

Answer

b

Answer

c

Answer

d

Question 20

Find the derivative of the given equation
f(x) = 1/x²

Accepted Answer

-2x-3

Answer

1/2x

Answer

-2x

Answer

2x

Question 21

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 22

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 23

The population of a town x years after 2000 is modeled by P(x).  What is the best interpretation of P'(10) = 50.

Accepted Answer

In 2010, the population was increasing 50 people per year.

Answer

In 2010, the population was 50 people.

Answer

It took 10 years for the population to increase by 50 people.

Answer

The average change in population over the 10 years was 50 people per year.

Question 24

Find the slope of f(x) = -3x²-6x at x = 1.

Accepted Answer

m = -12

Answer

m = 0

Answer

f'(x) = -6x - 6

Answer

f'(x) = 6x

Question 25

Set up the derivative of the equation

Accepted Answer

((x-3)-(x+2))/(x-3)²

Answer

((x+2)-(x-3)/(x-3)²

Answer

((x-3)-(x+2))/(x+2)²

Answer

((x+2)-(x-3)/(x+2)²

Question 26

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 27

Differentiate y= 12x^-2

Accepted Answer

-24x-3

Answer

24x-1

Answer

-24x-1

Answer

6x-3

Question 28

What is the derivative of g(x) = 4x³

Accepted Answer

12x2

Answer

12

Answer

4

Answer

3

Question 29

Find the derivative of the given equation
f(x) = x³ + x² + 3

Accepted Answer

3x2 + 2x

Answer

3x + 2x

Answer

3x + 2x + 3

Answer

x3 + x2

Question 30

What is the derivative of xⁿ?

Accepted Answer

nxn-1

Answer

(n-1)xn

Answer

nxn+1

Answer

(n+1)xn-1

Question 31

Find the derivative of the given equation
f(x) = 1/x²

Accepted Answer

-2x-3

Answer

1/2x

Answer

-2x

Answer

2x

Question 32

Differentiate f(x) =(2/ x⁵) - 5.

Accepted Answer

-10x-6

Answer

x5-3

Answer

-10x6

Answer

x5-5

Question 33

Find the derivative of:
sin(cos(2x-5))

Accepted Answer

-2cos(cos(2x-5))(sin(2x-5))

Answer

-2(sin²(2x-5))

Answer

-(cos(2x-5))(sin(2x-5)

Answer

2sinxcos(2x-5)

Question 34

What is f'(x) if f(x) = cos(5x⁴)?

Accepted Answer

f'(x) = -20x³ sin(5x⁴)

Answer

f'(x) = sin(20x³)

Answer

f'(x) = 20x³ sin(5x⁴)

Answer

f'(x) = -sin(20x³)

Question 35

Derive y=e^3x

Accepted Answer

3e3x

Answer

e3x

Answer

3x

Answer

3xe3x

Question 36

Find dy/dx by Implicit Differentiation
xy = 6

Accepted Answer

-y/ x

Answer

-x/ y

Answer

-6y/ x

Answer

y/x

Question 37

Find dy/dx
xy+y²=2

Accepted Answer

-y/(x+2y)

Answer

y/(x+2y)

Answer

-3y/x

Answer

-3x/y

Question 38

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

Question 39

Find the derivative:
y=5x²e^3x

Accepted Answer

y'=5xe^3x(3x+2)

Answer

y'=10xe^3x(2x+3)

Answer

y'=10ex^3x(3x+2)

Answer

y'=5xe^3x(2x+3)

Question 40

Find dy/dx by Implicit Differentiation
x + 4y = 1

Accepted Answer

-1/4

Answer

-1

Answer

4

Answer

1

Question 41

The function shown contains:

Accepted Answer

Two local maximums.

Answer

Only one local maximum.

Answer

Two local minimums.

Answer

Three local maximums

Question 42

When is this function increasing?

Accepted Answer

-3<x<3

Answer

-2.5<x<2.5

Answer

x>2.5

Answer

x>3

Question 43

Identify the critical points of the following function:
g(x)=2x³-3x²

Accepted Answer

x=0,1

Answer

x=-1,1

Answer

x=0,0

Answer

x=0,-1

Question 44

Find the critical points of f(x) = 2x⁴- 4x² + 1

Accepted Answer

x = -1, 0, 1

Answer

x= 0

Answer

x = -1, 1

Answer

no critical points

Question 45

How many relative maximums does this function have?

Accepted Answer

3

Answer

1

Answer

2

Answer

4

Question 46

How many relative minimums does this function have?

Accepted Answer

2

Answer

1

Answer

3

Answer

4

Question 47

Find the limit of the function as x approaches 2.

Accepted Answer

DNE

Answer

1

Answer

-1

Answer

5

Derivatives Practice

50 questions

Find the derivative of f(x) = 5x² + 7x - 3.

Differentiate y = -19

Differetiate y = -19x

Find the derivative:
y = (4x - 5)(2x + 3)

What is the derivative of sin(x)?

Find f '(2) if
f(x) = x² + 2x

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

Find dy/dx for
y = (x² + 1)³

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Derivatives Practice

50 questions

Find the derivative of f(x) = 5x2 + 7x - 3.

Differentiate y = -19

Differetiate y = -19x

Find the derivative:y = (4x - 5)(2x + 3)

What is the derivative of sin(x)?

Find f '(2) iff(x) = x2 + 2x

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

Find dy/dx for y = (x2 + 1)3

Create a free account and access millions of resources

Similar Resources on Wayground

Popular Resources on Wayground

Discover more resources for Mathematics

Find the derivative of f(x) = 5x² + 7x - 3.

Find the derivative:
y = (4x - 5)(2x + 3)

Find f '(2) if
f(x) = x² + 2x

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

Find dy/dx for
y = (x² + 1)³