Basic Derivative Rules 2.1-2.3 Flashcards

1

Find the derivative.

f'(x) = (-x2 + 6x + 1)/(x2 + 1)2
f'(x) = -x2 + 6x + 1
f'(x) = (-x2 - 6x + 1)/(x2 + 1)2
f'(x) = 1/(2x)

2

For what values of x does the graph of f(x)=x³ -6x² -36x+4 have horizontal tangents?

x = 3, x = 4
x = -6, x = 2
x = 6, x = -2
x = 3

3

Find the derivative

1
DNE
0
pi

4

Find the derivative.

f'(x) = 3x2 - 6x
f'(x) = -3x
f'(x) = 3x2 - 6
f'(x) = 0

5

Find the derivative.

f'(x) = 2x - 3 + 4/x
f'(x) = 3x - 3 + 2/x
f'(x) = 2 - 4/x2
y' = (6x2 - 6x + 4)/(2x)

6

What is d/dx[csc x]?

-csc x
-cot2 x
-cos2 x
-csc x cot x

7

Find the derivative.

f'(x) = 1 / x1/2 - 12x2 + 3 / x
f'(x) = 1 / (2x1/2) - 12x2 - 3 / x2
f'(x) = -1 / (2x3/2) - 12x2 + 3 / x2
f'(x) = -1 / (2x3/2) - 12x2 - 3 / x2

8

What is d/dx[sec x]?

sec x tan x
tan2 x
-csc x cot x
-csc2 x

9

Find the derivative.

f'(x) = 1 / (2x1/2) + 1 / (2x3/2)
f'(x) = (1/2)x - (-1/2)x
f'(x) = 1 / (2x1/2) - 1 / (2x3/2)
f'(x) = 1 / (2x)1/2 + 1 / (2x)3/2

10

What is d/dx[tan x]?

sec2 x
-csc x cot x
-csc2 x
sec x tan x

11

Find the derivative.

y' = 2 - 2xtan(x) - x2sec(x)tan(x)
y' = 2 - 2x sec(x)tan(x)
y' = 2 - 2xtan(x) - x2sec2(x)
y' = 2 - 2x sec2(x)

12

Find the derivative.

f'(t) = -3t2sin(t)
f'(t) = 3t2cos(t) - t3sin(t)
f'(t) = -3t2cos(t) + t3sin(t)
f'(t) = 3t2cos(t) + t3sin(t)

13

What would cause f(x) to have a horizontal tangent line?

If f '(x)=0
If f(x) is not differentiable.
If f(x) is undefined at that point
If f ' (x) is undefined

14

Find the derivative.

f'(t) = 3cos(t) - (1/4)sin(t)
f'(t) = -3sin(t) - (1/4)cos(t)
f'(t) = -3cos(t) + (1/4)sin(t)
f'(t) = 3sin(t) + (1/4)cos(t)

15

Find the derivative.

f'(t) = -4/(3t3)
f'(t) = 4/(3t3)
f'(t) = (-4/3)t3
f'(t) = (4/3)t

Basic Derivative Rules 2.1-2.3

Questions 15

Basic Derivative Rules 2.1-2.3

Questions 15