Chapter 4 Test Flashcards by Irina Soloshenko | Brainscape

Q

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

A

1

How well did you know this?

1

Not at all

2

3

4

5

Perfectly

Q

What is the derivative of the function

f (x) = 3x ^9?

A

27x^8

How well did you know this?

1

Not at all

2

3

4

5

Perfectly

Q

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

A

−2x ^2

How well did you know this?

1

Not at all

2

3

4

5

Perfectly

Q

Calculate f′(x) if f(x)=x^4+2x.

A

4x^3+2

How well did you know this?

1

Not at all

2

3

4

5

Perfectly

Q

What is the derivative of the function

f(x)=10/x^2+3/x^4−60x?

A

-20/x^3−12/x^5−60

How well did you know this?

1

Not at all

2

3

4

5

Perfectly

Q

What is the derivative of the function f(x)=√x+ ^3√x?

A

1/2x^−1/2+1/3x^−2/3

How well did you know this?

1

Not at all

2

3

4

5

Perfectly

Q

Compute the derivative of the function

f (x) = (5x^ 4 − 2x^ 2 + 7x + 4) (2x ^2 − 5).

A

(20x^ 3 − 4x + 7) (2x ^2 − 5) + 4x (5x^ 4 − 2x^ 2 + 7x + 4)

How well did you know this?

1

Not at all

2

3

4

5

Perfectly

Q

Compute the derivative of the function

f (x) = (2x ^2 + 3)^2.

A

8x (2x ^2 + 3)

How well did you know this?

1

Not at all

2

3

4

5

Perfectly

Q

Compute the derivative of the function

f (x) = (−x + 3x ^2 − x ^−2 )(3x − x^ −1 ).

A

(−1 + 6x + 2x ^−3 ) (3x − x^ −1 ) + (−x + 3x ^2 − x^ −2 ) (3 + x ^−2 )

How well did you know this?

1

Not at all

2

3

4

5

Perfectly

Q

Compute the derivative of the function

f(x)=x−x^2 / 3x+5.

A

(1−2x)(3x+5)−3(x−x^2) / (3x+5)^2

How well did you know this?

1

Not at all

2

3

4

5

Perfectly

Q

Compute the derivative of the function

f(x)=x^2+x−3 / x^3+5.

A

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

How well did you know this?

1

Not at all

2

3

4

5

Perfectly

Q

Compute the derivative of the function

f(x)=1/(x^2−1)^2.

A

−4x/(x^2−1)^3

How well did you know this?

1

Not at all

2

3

4

5

Perfectly

Q

Compute the derivative of the function

f(x)=x^3+3x^2−5 / √x+1.

A

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

How well did you know this?

1

Not at all

2

3

4

5

Perfectly

Q

Compute the derivative of the function

f(x) = (x^4 - 2x^2 + 7x + 4)^3

A

3(x^4−2x^2+7x+4)^2(4x^3−4x+7)`

How well did you know this?

1

Not at all

2

3

4

5

Perfectly

Q

Compute the derivative of the function

f(x)=(x+1 / x−1)^5

A

−10(x+1)^4 / (x−1)^6

How well did you know this?

1

Not at all

2

3

4

5

Perfectly

Q

Compute the derivative of the function

f(x)=(3x^2−x+1 / x^2+1)^7.

A

7(3x^2−x+1 / x^2+1)^6 (x^2+4x−1 / (x^2+1)^2)

Q

Compute the derivative of the function

f(x) = (4x^2-x+1)^7 (1+√x)

A

7(4x^2-x+1)^6(8x-1)(1+√x) + (4x^2-x+1)^7(1/2x^-1/2)

Q

Compute the derivative of the function

f(x)=2x / (3x^2+2)^3/2.

A

2(3x^2+2)^3/2−18x^2(3x^2+2)^1/2 / (3x^2+2)^3

Q

Compute the derivative of the function

f(x)=√x^2+1/x^2−1

A

-(x^2+1/x^2−1)^-1/2 * 2x(x^2−1)^2

Q

Compute dy/dx for y=(3x^2−x)^2 / 3−x^2

A

2(3x^2−x)(6x−1)(3−x^2)+2x(3x^2−x)^2(3−x^2)^2