Chapter 4 Practice Test

Question 1

What is the derivative of the function f (x) = 5?

Answer 1

0

Question 2

What is the derivative of the function f (x) = 2x?

Answer 2

2

Question 3

What is the derivative of the function f(x)=−1/4x^6?

Answer 3

3/2x^7

Question 4

Calculate f′(x) if f(x)=2x^9+8x^3+5.

Answer 4

18x ^8 + 24x ^2

Question 5

What is the derivative of the function f(x)=−6x^2−3x^2−6x?

Answer 5

−12x+6/x^3−6

Question 6

What is the derivative of the function f(x)=√x?

Answer 6

1/2√x

Question 7

Compute the derivative of the function f (x) = (2x ^2 + 3) (4x − 6).

Answer 7

4x (4x − 6) + 4 (2x^ 2 + 3)

Question 8

Compute the derivative of the function.

f(x)=(3x^2+1x)(2x^3−5x+7)

Answer 8

(6x−1/x^2)(2x^3−5x+7)+(3x^2+1x)(6x^2−5)

Question 9

Compute the derivative of the function f(x) = (−3x^4+5x^2−√x+3)(x^−2−6x)

Answer 9

(-12x^3+10x−1/2x^−1/2)(x^−2−6x) +(-3x^4+5x^2−√x+3)(-2x^−3−6)

Question 10

Compute the derivative of the function

f(x)=√x(4−x^2).

Answer 10

4−5x^2 / 2x^1/2

Question 11

Compute the derivative of the function

f(x)=x−1/x+1.

Answer 11

2/(x+1)^2

Question 12

Compute the derivative of the function

f(x)=1/x^2−x+2.

Answer 12

−2x+1 / (x^2−x+2)^2

Question 13

Compute the derivative of the function

f(x)=√x−1/√x+1.

Answer 13

1/√x(√x+1)^2

Question 14

Compute the derivative of the function f(x)=(x^2+x−3)^4

Answer 14

4(x^2+x−3)^3(2x+1)

Question 15

Compute the derivative of the function f(x)=(5x^3−4x+1/x)^6

Answer 15

6(5x^3−4x+1/x)^5(15x^2−4−x^−2)

Question 16

Compute the derivative of the function f(x) =

(x^2−3x+4 / 2x+3)10

Answer 16

(10(x^2−3x+4/2x+3)^9) (2x^2+6x−17/(2x+3)^2)

Question 17

Compute the derivative of the function

f(x)=(x^2−1)^4 / x^2+1.

Answer 17

2x(x^2−1)^3(3x^2+5) / (x^2+1)^2

Question 18

Compute the derivative of the function f(x)=1/√4x^2−5.

Answer 18

−4x / (4x^2−5)√4x^2−5

Question 19

Compute the derivative of the function f(x)=(x+1/x)^3/5

Answer 19

3/5(x+x^−1)^−2/5(1−x^−2)

Question 20

Compute the derivative of the function f(x)=(x^2−x)^3(3x+1) / x^4+2x^2−1.

Answer 20

(x^4+2x^2−1)[3(x^2−x)^2(2x−1)(3x+1) + 3(x^2−x)^3] −(x^2−x)^3(3x+1)(4x^3+4x) / (x^4+2x^2−1)^2