Derivatives and Integrals of Ln and e Flashcards

1

Find the derivative of y = 3x⁴

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

2

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

3

Find ∫ e^{2x - 1} dx

(2x-1)e2x-2
½ ex + C
½ e2x-1 + C
½ e2x-1

4

Differentiate y = (ln x)²

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

5

Find ∫ 1 / (3x+2) dx

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

6

Find ∫ e^3x dx

3e3x + C
1/3 e3x + C
1/3 ln |3x| +C
1/3 ex + C

7

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

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

8

Find the derivative of y = e^x

ex
x∙ex
ex + C
1/ex

9

Find the derivative of y = ln x⁴

1/x4 ∙ 4x3 + C
4/x · x4
4/x + C
4/x

10

Find the derivative of y = ln (5x²)

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

11

∫ 3x⁵ dx

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

12

Find ∫ 2e^2x dx

4e2x + C
½ e2x + C
e2x + C
4e2x

13

Find the derivative of y = 8e²

0
16e2
16e
undefined

14

∫ e^{6x + 2} dx

1/2 e6x + 2 + C
6e6x + 2 + C
1/6 e6x + 2 + C
1/6 e6x + 2

15

Differentiate y = 4x³ + 5x

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

Derivatives and Integrals of Ln and e

Questions 15

Derivatives and Integrals of Ln and e

Questions 15