Flashcard Set Preview
| Side A | Side B | ||
| 1 |
Derivative of a Constant
|
d/dx (c) = 0
|
|
| 2 |
Power Rule
|
d/dx (xn) = nxn-1
|
|
| 3 |
Constant Multiple Rule
|
d/dx [cf(x)] = cf'(x)
|
|
| 4 |
Sum Rule
|
d/dx [f(x) + g(x)] = f'(x) + g'(x)
|
|
| 5 |
Difference Rule
|
d/dx [f(x) - g(x)] = f'(x) - g'(x)
|
|
| 6 |
Product Rule
|
d/dx [f(x) g(x)] = f'(x) g(x) + g'(x) f(x)
|
|
| 7 |
Quotient Rule
|
d/dx [f(x)/g(x)] = [f'(x) g(x) - g'(x) f(x)]/[g(x)]2
|
|
| 8 |
Derivative of Sine
|
d/dx (sin x) = cos x
|
|
| 9 |
Derivative of Cosine
|
d/dx (cos x) = -sin x
|
|
| 10 |
Derivative of Tangent
|
d/dx (tan x) = sec2 x
|
|
| 11 |
Derivative of Cosecant
|
d/dx (csc x) = -csc x cot x
|
|
| 12 |
Derivative of Secant
|
d/dx (sec x) = sec x tan x
|
|
| 13 |
Derivative of Cotangent
|
d/dx (cot x) = -csc2 x
|
|
| 14 |
Chain Rule
|
d/dx {f[g(x)]} = f'[g(x)] g'(x)
|
|
| 15 |
Power Chain Rule
|
d/dx {[f(x)]n} = n[f(x)]n-1 f'(x)
|
|
| 16 |
Differential
|
dy = f'(x) dx
|
|
| 17 |
Inverse Function Theorem
|
d/dx [f-1(x)] = 1/f'[f-1(x)]
|
|
| 18 |
Exponential Addition
|
nx+y = nx ny
|
|
| 19 |
Exponential Subtraction
|
nx-y = nx/ny
|
|
| 20 |
Exponential Multiplication
|
nxy = (nx)y
|
|
| 21 |
Combinational Exponents
|
(cn)x = cx nx
|
|
| 22 |
Derivative of Natural Exponential Function
|
d/dx (enx) = nenx
|
|
| 23 |
Derivative of Logarithmic Functions
|
d/dx [ln f(x)] = f'(x)/f(x)
|
|
| 24 |
Linearization Formula
|
L(x) = f(a) + f'(a) (x - a)
|
|
| 25 |
Differentials
|
dy = f'(x) dx
|
|
| 26 |
Absolute Maximum
|
f(c) ≥ f(x) for all x in D
|
|
| 27 |
Absolute Minimum
|
f(c) ≤ f(x) for all x in D
|
|
| 28 |
Local Maximum
|
f(c) ≥ f(x) when x is near c
|
|
| 29 |
Local Minimum
|
f(c) ≤ f(x) when x is near c
|
|
| 30 |
Mean Value Theorem
|
f'(c) = [f(b) - f(a)]/(a - b)
|
|
| 31 |
Increasing Function
|
f'(x) > 0
|
|
| 32 |
Decreasing Function
|
f'(x) < 0
|
|
| 33 |
Concave Up
|
f"(x) > 0
|
|
| 34 |
Concave Down
|
f"(x) < 0
|
|
| 35 |
Local Minimum II
|
f'(x) = 0 and f"(x) > 0
|
|
| 36 |
Local Maximum II
|
f'(x) = 0 and f"(x) < 0
|
|
| 37 |
Horizontal Asymptotes
|
f(x) => H as x => ∞ or -∞
|
|
| 38 |
Vertical Asymptotes
|
f(x) => ∞ or -∞ as x => V
|
|
| 39 |
Even Function
|
f(-x) = f(x) for all x in D
|
|
| 40 |
Odd Function
|
f(-x) = f(-x) for all x in D
|
|
| 41 |
Periodic Function
|
f(x + p) = f(x) for all x in D
|
|
| 42 |
Newton's Method
|
xn+1 = xn - f(xn)/f'(xn)
|
|
| 43 |
Moving Upwards
|
f(x) + c
|
|
| 44 |
Moving Downwards
|
f(x) - c
|
|
| 45 |
Moving RIghtwards
|
f(x - c)
|
|
| 46 |
Moving Leftwards
|
f(x + c)
|
|
| 47 |
Vertical Stretching
|
cf(x)
|
|
| 48 |
Vertical Shrinking
|
f(x)/c
|
|
| 49 |
Horizontal Shrinking
|
f(cx)
|
|
| 50 |
Horizontal Stretching
|
f(x/c)
|
|
| 51 |
Vertical Reflecting
|
-f(x)
|
|
| 52 |
Horizontal Reflecting
|
f(-x)
|
|
| 53 |
Limit Law #1
|
lim [f(x) + g(x)] = lim f(x) + lim g(x)
|
|
| 54 |
Limit Law #2
|
lim [f(x) - g(x)] = lim f(x) - lim g(x)
|
|
| 55 |
Limit Law #3
|
lim [cf(x)] = c lim f(x)
|
|
| 56 |
Limit Law #4
|
lim [f(x) g(x)] = lim f(x) lim g(x)
|
|
| 57 |
Limit Law #5
|
lim [f(x)/g(x)] = lim f(x)/lim g(x)
|
|
| 58 |
Limit Law #6
|
lim [f(x)n] = [lim f(x)]n
|
|
| 59 |
Limit Law #7
|
lim c = c
|
|
| 60 |
Limit Law #8
|
lim x = a
|
|
| 61 |
Limit Law #9
|
lim xn = an
|
|
| 62 |
LImit Law #10
|
lim x1/n = a1/n
|
|
| 63 |
Limit Law #11
|
lim [f(x)1/n] = [lim f(x)]1/n
|
No comments yet! Be the first to add a comment below!
Please login to post comments.
After login, we will forward you back to this flashcard.