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Basic Derivative Rules Flashcards | StudBud

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Basic Derivative Rules

11 terms·StudBud Administration·47 plays

Quiz over the basic derivative rules including power, product, quotient & chain rule.

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Questions 11

Answers

1
Find the derivative.
f'(x) = 1/(2x)1/2 + 1/(2x)3/2
f'(x) = 1/(2x1/2) + 1/(2x3/2)
f'(x) = (1/2)x - (-1/2)x
f'(x) = 1/(2x1/2) - 1/(2x3/2)
2
Find the derivative.
f'(x) = 2x - 3 + 4/x
f'(x) = 2 - 4/x2
f'(x) = 3x - 3 + 2/x
y' = (6x2 - 6x + 4)/(2x)
3
Find the derivative.
y' = (2x)(x2 - 1)2(4x2 - 1)]
y' = (x2 - 1)2[2x(x2 - 1) + 3x2]
Nope
y' = 12x2(x2 - 1)2
4
Find the derivative
0
1
DNE
pi
5
Find the derivative.
f'(x) = (-x2 + 6x + 1)/(x2 + 1)2
f'(x) = (-x2 - 6x + 1)/(x2 + 1)2
f'(x) = -x2 + 6x + 1
f'(x) = 1/(2x)
6
Horizontal tangents?
x = 6, x = -2
x = -6, x = 2
x = 3, x = 4
x = 3
7
Find the derivative.
f'(t) = (4/3)t
f'(t) = (-4/3)t3
f'(t) = -4/(3t3)
f'(t) = 4/(3t3)
8
Find the derivative.
f'(x) = (1/2)/(1 - x3)1/2
f'(x) = (1-x3)1/2
f'(x) = -3x2/[2(1 - x3)1/2]
f'(x) = sqr(-3x2)
9
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
10
Find the derivative.
f'(x) = 3x2 - 6
f'(x) = 0
f'(x) = 3x2 - 6x
f'(x) = -3x
11
Find the average rate of change.
-3/2
1/2
3/2
1