Review of Basic Derivative Rules Flashcards

1

Find the equation of the tangent line.

y = 0
y = 1
y = πx
vertical line

2

Find the derivative.

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

3

Find the derivative.

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

4

Find the derivative.

Nope
y' = (x2 - 1)2[2x(x2 - 1) + 3x2]
y' = 12x2(x2 - 1)2
y' = (2x)(x2 - 1)2(4x2 - 1)]

5

Find the derivative

1
0
DNE
pi

6

Find the derivative.

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

7

Find the derivative.

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

8

Find the derivative.

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

9

Find the derivative.

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

10

Find the derivative.

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

11

Find the average rate of change for y = -1/x on the interval [1, 2].

3/2
-3/2
1
1/2

12

When does y = x³ - 6x² -36x +4 have Horizontal tangents?

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

13

Find the derivative.

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

14

Find the derivative.

f'(x) = (1/2)/(1 - x3)1/2
f'(x) = -3x2/[2(1 - x3)1/2]
f'(x) = (1-x3)1/2
f'(x) = sqr(-3x2)

15

Find the derivative.

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

Review of Basic Derivative Rules

Questions 15

Review of Basic Derivative Rules

Questions 15