Chapter 4 Test Flashcards Preview

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Flashcards in Chapter 4 Test Deck (20):
1

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

1

2

What is the derivative of the function
f (x) = 3x ^9?

27x^8

3

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

−2x ^2

4

Calculate f′(x) if f(x)=x^4+2x.

4x^3+2

5

What is the derivative of the function
f(x)=10/x^2+3/x^4−60x?

-20/x^3−12/x^5−60

6

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

1/2x^−1/2+1/3x^−2/3

7

Compute the derivative of the function
f (x) = (5x^ 4 − 2x^ 2 + 7x + 4) (2x ^2 − 5).

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

8

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

8x (2x ^2 + 3)

9

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

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

10

Compute the derivative of the function
f(x)=x−x^2 / 3x+5.

(1−2x)(3x+5)−3(x−x^2) / (3x+5)^2

11

Compute the derivative of the function
f(x)=x^2+x−3 / x^3+5.

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

12

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

−4x/(x^2−1)^3

13

Compute the derivative of the function
f(x)=x^3+3x^2−5 / √x+1.

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

14

Compute the derivative of the function
f(x) = (x^4 - 2x^2 + 7x + 4)^3

3(x^4−2x^2+7x+4)^2(4x^3−4x+7)`

15

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

−10(x+1)^4 / (x−1)^6

16

Compute the derivative of the function
f(x)=(3x^2−x+1 / x^2+1)^7.

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

17

Compute the derivative of the function
f(x) = (4x^2-x+1)^7 (1+√x)

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

18

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

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

19

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

-(x^2+1/x^2−1)^-1/2 * 2x(x^2−1)^2

20

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

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

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