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Calculus: Derivatives Flashcards | StudBud
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Calculus: Derivatives
Calculus: Derivatives
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A review of the different types of #derivatives in AP Calculus AB and BC
Flashcards
20 cards
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Practice quiz
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Questions
20
Answers
1
What is the derivative of tan
-1
(x)?
-1/√1-x2
1/ƖxƖ√x2-1
1/1+x2
1/√1-x2
2
What is the derivative of e
u
?
dy/dx
eu
1/u
eudu
3
What is the product rule?
f(x)⋅f'(x) + g(x)⋅g'(x)
f'(x)/g'(x)
f(x)⋅g'(x) + g(x)⋅f'(x)
f'(x)⋅g'(x)
4
What is the derivative of csc(x)?
5
sinx/tanx
-cosxcotx
-cscxcotx
5
What is the derivative of cos(x)?
-sinx
sinx
cosx
-cosx
6
What is the derivative of a
u
?
lna
audu
1/a
aulna du
7
What is the derivative of y
2
?
5t
y3/3
2y
y
8
What is the derivative of tan(x)?
cos2x
secx
sinx
sec2x
9
What is the quotient rule, using f(x)/g(x)?
f(x)⋅g'(x) - g(x)⋅f'(x)/ f(x)⋅g(x)
g(x)⋅f'(x) - f(x)⋅g'(x)/ g(x)⋅g(x)
f'(x)/g'(x)
ho⋅d(hi)- hi⋅d(ho)/ho⋅ho
10
What is the derivative of 5x
3
+17x
2
-5
15x4+17x3-5x
5x2+17x-5
15x2+34x+C
15x2+34x
11
What is a derivative?
Rate of change
The number of points on a graph
The shape of a function
Slope
12
What is the derivative of ln(u)?
du/u
ln0(u)
1/u ×du
1/u +C
13
What is the power rule?
(xn)'= xn+1/n+1
2y
(xn)'=nx
(xn)'=n(x)n-1
14
What is the derivative of sin(x)?
tanx
cscx
-cosx
cosx
15
What is the chain rule?
(f⋅g)'=f'(x)g'(x)
(f⋅g)'=f'(g(x))(g'(x))
(f⋅g)'=f(x)g'(x)+g(x)f'(x)
(f⋅g)'=g'(g(x))(f'(x))
16
What is the derivative of sec(x)?
cotx
sec2xtanx
secxtanx
sinx
17
What is the derivative of sec
-1
(x)?
-1/√1-x2
1/√1-x2
1/ƖxƖ√x2-1
1/1+x2
18
What is the derivative of cos
-1
(x)?
1/ƖxƖ√x2-1
-1/√1-x2
1/1+x2
1/√1-x2
19
What is the derivative of cot(x)?
cscxtanx
-1/sin2x
-csc2x
xtoc
20
What is the derivative of sin
-1
(x)?
1/1+x2
-1/√1-x2
1/√1-x2
1/ƖxƖ√x2-1
