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Basic Derivative Rules Flashcards | StudBud

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Basic Derivative Rules

14 terms·StudBud Administration·26 plays

Quiz over the basic derivative rules including power, product, quotient as well as sin, cos, tan

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Questions 14

Answers

1
Find the derivative.
f'(t) = 3sin(t) + (1/4)cos(t)
f'(t) = 3cos(t) - (1/4)sin(t)
f'(t) = -3cos(t) + (1/4)sin(t)
f'(t) = -3sin(t) - (1/4)cos(t)
2
Find the average rate of change.
1
3/2
-3/2
1/2
3
What is the instanteneous rate of change at x=2 of f(x) = (x² - 2) / (x - 1)?
2
-2
1/6
6
4
Find the derivative.
f'(x) = (1/2)x - (-1/2)x
f'(x) = 1/(2x)1/2 + 1/(2x)3/2
f'(x) = 1/(2x1/2) - 1/(2x3/2)
f'(x) = 1/(2x1/2) + 1/(2x3/2)
5
Horizontal tangents?
x = 3
x = 6, x = -2
x = 3, x = 4
x = -6, x = 2
6
Find the derivative.
f'(x) = -x2 + 6x + 1
f'(x) = 1/(2x)
f'(x) = (-x2 + 6x + 1)/(x2 + 1)
f'(x) = (-x2 - 6x + 1)/(x2 + 1)
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'(t) = 3t2cos(t) + t3sin(t)
f'(t) = -3t2cos(t) + t3sin(t)
f'(t) = 3t2cos(t) - t3sin(t)
f'(t) = -3t2sin(t)
9
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)
10
Find the derivative.
f'(x) = -3x
f'(x) = 3x2 - 6x
f'(x) = 0
f'(x) = 3x2 - 6
11
Find the equation of the tangent line.
vertical line
y = 0
y = 1
y = πx
12
Find the derivative
DNE
pi
0
1
13
Find the derivative.
f'(x) = x-1/2 - 12x2 + 3x-1
f'(x) = -1/(2x3/2) - 12x2 + 3/x2
f'(x) = 1/(2x1/2) - 12x2 - 3/x2
f'(x) = -1/(2x3/2) - 12x2 - 3/x2
14
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)