Derivatives and Antiderivatives Flashcards

1

Find the derivative of the function f(x) = (5x²+5)⁶

6(5x)6
None of these
6(5x2+5)5
60x(5x2+5)5

2

∫550 dx =

550x
0
550x + C
None of these

3

The Intermediate Value Theorem cannot be applied to which of these functions on [-5, 5]?

sinxcosx
secx
x5 + 3x+7
None of these

4

Find the antiderivative of sinx.

None of these
-sinx + C
cosx + c
-cosx + C

5

Find the derivative of cotx.

csc2x + C
-csc2x + C
None of these
-csc2x

6

Find the particular solution of f(x) = ∫4x²dx if F(1) = 2.

(4/3)x3 + C
4x2 + (2/3)
(4/3)x3 + (2/3)
None of these

7

Which of the following integration rules is correct?

∫0dx = C
∫k dx = k + C
None of these
∫(secxtanx)dx = cscx + C

8

d/dx(sin²3x) =

6(sin3x)(cos3x)
None of these
cos23x
-3(sin3x)(cos3x)

9

d/dx[velocity] =

acceleration
position
None of these
velocity

10

Which of the following relationships is correct?

∫(acceleration)dt = velocity
∫(velocity)dt = acceleration
∫(position)dt = velocity
None of these

11

f'(x) = 3x, F(x) =

3x2 + C
3/2 x2
None of these
6x2 + C

12

How many antiderivatives does f(x) = secxtanx + 5x³ have?

An infinite number
None
None of these
Exactly 1

13

The derivative of tanx =

secxtanx
tan2x
-cotx
None of these

14

Find the derivative of sinx.

sinx
cosx
None of these
-cosx

15

d/dx[secx] =

-sinx
-cscxcotx
None of these
sec2x

16

∫(3x + 6x⁵)dx =

3/2x2 + x6 + C
3/2x2 + x6
None of these
2x2+(1/6)x6 + C

Derivatives and Antiderivatives

Questions 16

Derivatives and Antiderivatives

Questions 16