differentiation Flashcards
d/dx
differentiation symbol
polynomial
d/dx(polynomial)
d/dx(X)
1
d/dx(1/x)
-1/x^2
d/dx(-1/x)
1/x^2
d/dx(3)
0
1/ square root of x
x^-1/2
1/x can be written as
x^-1
d/dx(ax+b)^n
n(ax+b)^n-1 * a
d/dx( square root ax+b)
1/2square root ax+b * a
dy/dx is AKA
fâ(X)
tangent and normal are
perpendicular to eachother m1 * m2 = -1
equation of a line
y-y1=m(x-x1)
the chain rule is used for
3 variables
d/dt
rate of change
if y= f(X)
dy/dt= dy/dx * dx/dt
if v=f(l)
v/t = v/l * l/t so v=l^3
if A=f(r)
A/t= A/r * r/t so A=Pir^2
if dy/dt is positive
its said that y increases at t increases
if dy/dt is negative
its said that y decreases as t decreases
dy/dt=
rate of change of y
the gradient of stationary points
0
stationary value
y coordinate of turning point
stationary point
min and max turning point
to find nature of stationary points and values
use second deravitive
d^2y/dx^2
second derivative AKA fââ(x)
if d^2y/dx^2 is +ve
its a min point
if d^2y/dx^2 is -ve
max TP
sphere volume
SA of a sphere
hemisphere volume
closed hemisphere SA
open hemisphere SA
cube volume
l^3
cube surface area
6l^3
cuboid volume
lbh
cuboid closed SA
cuboid open SA
cone volume
cone curved surface area
cone surface area
slant length of cone=
square root h^2 +r^2
cone
for similar cones
cylinder volume
cylinder curved surface area
cylinder total closed surface area
cylinder open total surface area
prism volume
prism TSA
prism perimeter
prism
pyramid volume
1/3 * base area * hieght
pyramid TSA
