Derivatives and Integrals of Ln and e Flashcards

1

Find ∫ 1 / (3x+2) dx

(ln |3x+2|)/3
(ln |3x+2|)/3 + C
(ln |3x+2|) + C
(ln |u|)/3 + C

2

Find the derivative of y = ln5x

1/x
1/5x
1/10x
5x/1

3

Find the area under y = 1/x from x = 3 to x = 9

ln 3 - ln 9 sq units
- 2/9 sq units
e9 - e3 sq units
ln 3 sq units

4

Find ∫ x/(3x²+1) dx

(6x)/(3x2+1)
6 ln |3x2+1| + C
1/6 ln |3x2+1| + C
1/6 |3x2+1| + C

5

Find the derivative of e^3x

9e3x
1/3 ex
3e3x
ln 3x

6

Differentiate y = (ln x)²

(2 ln x) / x
2/x
(ln x) / x
2 ln x

7

Find the derivative of y = 8e²

undefined
0
16e
16e2

8

Using log rules, which expression is equivalent to ln(x²y³z)

2ln x + 3ln y + ln z
2ln x + 3ln y + 4ln z
6(ln x + ln y + ln z)
1/x + 1/y + 1/z

9

Differentiate y = 4x³ + 5x

12x2 + 5
x/4 + 5x2 + C
x/4 + 5x2
12x2 + 5 + C

10

Find the derivative of y = x∙e^x

xex + 1
(1) ∙ ex
xex + ex
ex

11

Find the derivative of y = e^{4x^3}

12xe4x^3
12x2e4x^3
ln|4x3|
e4x^3

12

Find the derivative of y = (ln x)³

3(ln x)2
3(ln x)2∙ 1/x
3(ln x) 1/x
3/x

13

Find the derivative of y = 3x⁴

x5/5
12x3
4x3/3
x5/5 + C

14

∫ 5/xdx

1/x + C
5ln|5x| + C
5 ln|x| + C
5ex + C

15

Find the derivative of y = ln (5x²)

2/x2
1/(5x2)
10x
2/x

16

Find ∫ 1/(5x+1) dx

5/(5x + 1)
1/5 (5x+1) + C
1/5 ln | (5x+1) | +C
1/5 | ln (5x+1) | +C

17

Find the derivative of e^{2x - 1}

2e2x-1
½ e2x-1
½ ex
(2x-1)e2x-1

18

Find the derivative of y = ln x⁴

4/x · x4
4/x + C
1/x4 ∙ 4x3 + C
4/x

19

Find the derivative of y = e^x

ex
1/ex
ex + C
x∙ex

20

∫ 3x⁵ dx

x6/2 + C
x6/2
x5/2 + C
x6/6 + C

Derivatives and Integrals of Ln and e

Questions 20

Derivatives and Integrals of Ln and e

Questions 20