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AP Calculus AB Chapter 4 Derivatives Flashcards | StudBud
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AP Calculus AB Chapter 4 Derivatives
AP Calculus AB Chapter 4 Derivatives
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1
Power Rule for Arbitrary Real Power
d/dx (u-v) = du/dx -dv/dx
d/dx (Un) = nun-1du/dx
d/dx (c) = 0
d/dx (u+v) = du/dx + dv/dx
2
d/dx of csc^-1 x
1/|x|√x^2-1
-1/1+x^2
-1/|x|√x^2-1
1/1+x^2
3
d/dx of cot x
cos x
-csc x cot x
sec^2 x
-csc^2 x
4
d/dx cos x
- sin x
sec^2 x
-csc^2 x
sec x tan x
5
d/dx of ln x
ax ln a
1/x ln a
ex
1/x
6
Product Rule
d/dx (cu)= c du/dx
d/dx (uv) = U dv/dx + V du/dx
d/dx (u - v) = du/dx - dv/dx
d/dx (un) = nun-1 du/dx
7
Constant Multiple Rule
d/dx (u - v) = du/dx - dv/dx
d/dx (un) = nun-1 du/dx
d/dx (cu) = c du/dx
d/dx (c) = 0
8
Difference Rule
d/dx (cu)= c du/dx
d/dx (un) = nun-1 du/dx
d/dx (u - v) = du/dx - dv/dx
d/dx (uv) = u dv/dx + v du/dx
9
d/dx of csc x
sec x tan x
sec^2x
-csc x cot x
cos x
10
Quotient Rule
d/dx (uv) = U dv/dx + V du/dx
d/dx (un) = nun-1 du/dx
d/dx (cu)= c du/dx
d/dx (u/v) = V du/dx - U dv/dx / V2
11
d/dx of (sin^-1x)
1/√1-x
-1/1-x^2
1/1+x^2
1/√1-x^2
12
d/dx of (e^x)
a^x ln a
1/x
1/x ln a
e^x
13
d/dx of tan x
-sin x
-csc^2 x
cos x
sec^2 x
14
d/dx of Sin x
sec^2 x
-sin x
cos x
-csc x cot x
15
d/dx log
a
x
1/x ln a
ex
1/x
ax ln a
16
d/dx of sec x
sec x tan x
-csc x cot x
-csc^2 x
sec^2 x
17
d/dx of tan^-1 x
-1/√1+x^2
1/1+x^2
-1/|x|√x^2-1
-1/1+x^2
18
d/dx of a^x
1/x
a^x ln x
1/x ln a
e^x
19
d/dx of sec^-1 x
1/1+x
1/1+x^2
1/|x|√x^2-1
1/√1-x^2
20
Constant Rule
d/dx (un) = nun-1 du/dx
d/dx (Xn) = nxn-1
d/dx (cu) = c du/dx
d/dx (c) = 0
21
Chain Rule
d/dx (u + v) = du/dx + dv/dx
d/dx [f(g(x)] = f'(g(x)) * g'(x)
d/dx (u/v) = V du/dx - U dv/dx / V2
d/dx (Xn) = nxn-1
22
d/dx of cot^-1 x
-1/1+x^2
1/√1+x^2
1/|x|√x^2-1
1/1+x^2
23
Power Rule for Negative Integer Powers of x
d/dx [f(g(x)] = f'(g(x)) * g'(x)
d/dx (un) = nun-1 du/dx
d/dx (u/v) = V du/dx - U dv/dx / V2
d/dx (Xn) = nxn-1
24
Sum Rule
d/dx (uv) = u dv/dx + v du/dx
d/dx (cu)= c du/dx
d/dx (u - v) = du/dx - dv/dx
d/dx (u + v) = du/dx + dv/dx
25
d/dx of cos^-1 x
-1/√1-x^2
-1/1-x^2
-1/1+x^2
1/|x|√x^2-1
