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Derivatives Notes
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Summary based on coursework in the Engineering Maths 115 course at Stellenbosch University. Used for Tutoring Purposes on Teachme2.
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Antiderivatives
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Advanced Calculus Mathematics 214
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Early Transcendentals Appendix A, B, C
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Differential Calculus-
¥;
y y=mxtc
y
BY
•
.
¥ "
.
.
x
x i
x
slope =AI=m ^ "
*
Average slope
of change)
* Instantaneous
change
rate of
( race
¥
Derivative
Notation
-
order I order 2
-
order n
¥7
-
-
hiebniz / Differential Notation : It
"
dxz DX
f
" '
Gc ) f
'
Notation Cx )
"
f Gc )
Lagrange
:
notations
"
Other Ej :
or
y ij
' '
N IA
or y
T A
more more
Common common
in
Physics in math
Higher order derivatives
I¥z=¥G¥I
f
"
G) =
¥ Cfkx ))
fi G)
"
# I f
" '
Cx) ]
Intuitively
-
'
=
-
¥m¥m
on ← dependent SGD
← independent Cx )
* hess * Steeper
steep
slope Slope
, fed
Differentiability
ta
-
.
* If a function 's derivative particular
exists at a
point ,
then it is differentiable that * fcx ) is differentiable
at
point @ sea
Definition of derivative → Derivatives from first
-
principles
①
# i÷÷
fcx )
f Cx) -
fca ) Ag
Has -
-
Esa ⇒ .
r i
a K
This gap approaches
x
Z er as
② approaches a
f- Cath ) Ha ) Aye
tin
-
→
' -
ax
f (a) =
h⇒o
h
f Cath ) . - - - - - .
a ath
. X
in
h
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