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FORMULA DBM20023 Flipbook PDF
FORMULA DBM20023
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FORMULA SHEET FOR DBM20023 EXPONENTS AND LOGARITHMS LAW OF EXPONENTS
LAW OF LOGARITHMS
1.
ππ Γ ππ = ππ+π
8.
logπ π = 1
2.
ππ = ππβπ ππ
9.
logπ 1 = 0
3.
(ππ)π = ππΓπ
10.
logπ π =
4.
π0 = 1
11.
logπ ππ = logπ π + logπ π
5.
πβπ =
12.
logπ
6.
π π = ( βπ)π
13.
logπ ππ = π logπ π
7.
(ππ)π = ππππ
14.
π = ππ₯ β logπ π = π₯
π
1 ππ
,πβ 0
π
logπ π log ππ
π = logπ π β logπ π π
DIFFERENTIATION 1.
3.
5.
7.
9.
11.
13.
15.
π
ππ₯
[π] = 0
π ππ₯ π ππ₯ π ππ₯ π ππ₯ π ππ₯ π ππ₯
, k is constant
2.
[π(π₯) Β± π(π₯)] = πβ²(π₯) Β± πβ²(π₯)
4.
[πππ’(π₯)] = πππ’(π₯) Β· π’β²(π₯)
6.
[π sin π’(π₯)] = π cos π’(π₯) Β· π’β²(π₯)
8.
[π cos π’(π₯)] = βπ sin π’(π₯) Β· π’β²(π₯)
10.
[π tan π’(π₯)] = π π ππ2 π’(π₯) Β· π’β²(π₯)
12.
[π¦{π’(π₯)}] =
ππ¦
Γ
ππ’
ππ’ ππ₯ ππ’ β π’ ππ£) (π£ ππ₯ π π’(π₯) ππ₯ [ ]= 2 (π£) ππ₯ π£(π₯)
[Chain Rule]
14.
[Quotient Rule]
16.
π ππ₯ π
[ ππ₯π] = πππ₯πβ1
[Power Rule]
[π{π’(π₯)}π] = ππ{π’(π₯)}πβ1 Β· π’β²(π₯) [Composite]
ππ₯
π ππ₯ π ππ₯ π
π ππ₯ π
π π’( π₯ )
Β· π’β²(π₯)
[π sinπ π’(π₯)] = π cos π’(π₯) Β· sinπβ1 π’(π₯) Β· π’β²(π₯)
[π cosπ π’(π₯)] = βπ sin π’(π₯) Β· cosπβ1 π’(π₯) Β· π’β²(π₯)
ππ₯
ππ₯
[πln π’(π₯)] =
[π tanπ π’(π₯)] = π tanπβ1 π’(π₯) Β· π ππ2 π’(π₯) Β· π’β²(π₯)
[π’(π₯) Β· π£(π₯)] = π’
ππ¦(π‘) ππ₯(π‘)
=
ππ¦(π‘) ππ‘
Γ
ππ‘ ππ₯(π‘)
ππ£ ππ₯
+π£
ππ’ ππ₯
[Product Rule]
[Parametric Equation]
INTEGRATION 1.
β« π ππ₯ = ππ₯ + π
, k is constant
3.
β«[π(π₯) Β± π(π₯)] ππ₯ = β« π(π₯) ππ₯ Β± β« π(π₯) ππ₯
β« ππ₯ πππ₯ =
4.
β« π[π’(π₯)]πππ₯ =
6.
β«
8.
β« π π ππ π’( π₯) ππ₯ = β
10.
β« π π ππ2 π’( π₯) ππ₯ =
π
5.
β« π(π₯)ππ₯ = πΉ(π) β πΉ(π) π
ππ’(π₯)
7.
β« ππ’(π₯) ππ₯ =
9.
β« π πππ π’(π₯)ππ₯ =
π’β²(π₯)
+π π π ππ π’(π₯) π’ β²( π₯ )
+π
ππ₯π+1 + π ; {π β β1} ( π + 1)
2.
π[π’(π₯)]π+1 (π + 1) Β· π’β²(π₯)
π π ln[π’(π₯)] ππ₯ = [π’(π₯)]π π’β²(π₯)
1.
πππ 2 π + π ππ2 π = 1
2.
1 + π‘ππ2 π = π ππ2 π
3.
1 + πππ‘2π = πππ ππ2 π
4.
sin 2π = 2 sin π cos π
6.
tan 2π =
8.
cot π =
10.
πππ ππ π =
5. 7. 9.
cos 2π = 2 πππ 2π β 1 = 1 β 2 π ππ2π = πππ 2π β π ππ2π sin π tan π = cos π sec π =
1 cos π
2 tan π 1 β π‘ππ2 π
cos π sin π
=
1 tan π
1 sin π
AREA UNDER CURVE π
1.
π
π΄π₯ = β« π¦ ππ₯
2.
π
π΄π¦ = β« π₯ ππ¦ π
VOLUME UNDER CURVE π
1.
ππ₯ = π β« π¦2 ππ₯ π
π
2.
ππ¦ = π β« π₯2 ππ¦ π
INTEGRATION BY PARTS β« π’ ππ£ = π’π£ β β« π£ ππ’
π’β²(π₯)
π π‘ππ π’(π₯)
IDENTITY TRIGONOMETRY
; {π β β1}
; {π = 1}
π πππ π’(π₯)
π’β²(π₯)
+π
+π
+π