differentiation Flashcards
(58 cards)
1
Q
d/dx
A
differentiation symbol
2
Q
A
polynomial
3
Q
d/dx(polynomial)
A
4
Q
A
5
Q
d/dx(X)
A
1
6
Q
d/dx(1/x)
A
-1/x^2
7
Q
d/dx(-1/x)
A
1/x^2
8
Q
d/dx(3)
A
0
9
Q
1/ square root of x
A
x^-1/2
10
Q
1/x can be written as
A
x^-1
11
Q
d/dx(ax+b)^n
A
n(ax+b)^n-1 * a
12
Q
d/dx( square root ax+b)
A
1/2square root ax+b * a
13
Q
dy/dx is AKA
A
fâ(X)
14
Q
tangent and normal are
A
perpendicular to eachother m1 * m2 = -1
15
Q
equation of a line
A
y-y1=m(x-x1)
16
Q
the chain rule is used for
A
3 variables
17
Q
d/dt
A
rate of change
18
Q
if y= f(X)
A
dy/dt= dy/dx * dx/dt
19
Q
if v=f(l)
A
v/t = v/l * l/t so v=l^3
20
Q
if A=f(r)
A
A/t= A/r * r/t so A=Pir^2
21
Q
if dy/dt is positive
A
its said that y increases at t increases
22
Q
if dy/dt is negative
A
its said that y decreases as t decreases
23
Q
dy/dt=
A
rate of change of y
24
Q
the gradient of stationary points
A
0
25
stationary value
y coordinate of turning point
26
stationary point
min and max turning point
27
to find nature of stationary points and values
use second deravitive
28
d^2y/dx^2
second derivative AKA f''(x)
29
if d^2y/dx^2 is +ve
its a min point
30
if d^2y/dx^2 is -ve
max TP
31
sphere volume
32
SA of a sphere
33
hemisphere volume
34
closed hemisphere SA
35
open hemisphere SA
36
cube volume
l^3
37
cube surface area
6l^3
38
cuboid volume
l*b*h
39
cuboid closed SA
40
cuboid open SA
41
cone volume
42
cone curved surface area
43
cone surface area
44
slant length of cone=
square root h^2 +r^2
45
cone
46
for similar cones
47
cylinder volume
48
cylinder curved surface area
49
cylinder total closed surface area
50
cylinder open total surface area
51
prism volume
52
prism TSA
53
prism perimeter
54
prism
55
pyramid volume
1/3 * base area * hieght
56
pyramid TSA
57
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