Summary
Summary Differentiation
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A full summary of Differentiation for year 1 and 2 of A-Levels.
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Differentiationcontents :
-
General rule
and normals
Tangents
-
-
increasing / decreasing functions
-
second order derivatives
-
stationary points
-
gradient functions
-
first principles
-
non -
polynomials
-
product rule
-
quotient rule
-
Chain rule
-
implicit differentiation
trig functions
-
-
differential equations
-
General solution
-
rates of change
-
sins and cos ×
Disclaimer : I
got an
① using these notes in A-level maths
, DIFFERENTIATION
differentiation chi
CH1
rule
The
gradient of a curve is
constantly changing .
you can General
"
"
use a
tangent to find the gradient of a curve if y
=
ax ,
then
¥,
= an x
at any point on the curve .
multiply by the power then
-
the gradient of a curve at a
given point is minus one from the power .
defined as the gradient of the tangent to
the curve at that point .
functions with two or more terms
-
the gradient function ,
or derivative , of the curve let f- 1×1 =
4×2-8×+3
y=f( ) written as f Isc )
'
F4C)
x is or
dig 8×-8
=
.
consider each term individually .
x=flx) ¥=flx)
'
Equations of tangents and Normals .
fix) →
f- Isc) = →
the normal to a curve at the point A is the
line
straight through A which is perpendicular to
ny
µ
the
tangent .
gradient of tangent =
day
=m
gradient of normal = -
Imo Jc
increasing $ decreasing functions
A function is
increasing when the gradient is second order derivatives
find the
positive
day rate change the
> o you can of of
gradient function by differentiating a
A function is
decreasing when the gradient is function twice .
negative dy_ < 0
DX
y= 5×3 day 15×2 d¥
>
= > =
30k
, '
dx
stationary points
T
A
stationary point is a point
on the curve where the gradient this is the rate of
is 0 .
In some cases
you can use change of the
gradient
dy_=o the second derivative to
doc
determine the nature of a
There are three types of stationary stationary point .
points .
-
maximum
-
minimum if Ey > o the s.p.is a min .
doit
-
points of inflection
if dI < 0 the s.p.is a Max .
my da
'
if point
dd¥ stationary
=o ,
the
,
could be a Max min , or point
:
,
inflection
.
of .
Jun .
will need to look at points
you
either side to determine its nature .
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