# अवकलन के सूत्र तथा सीमाओं का प्रसार ( Formulas of Differentiation )

Here Are Some Important Formulas Of Differentiation. These Formulas are very important for those students who are related to Mathematics or physics.So here we provide The PDF File of these very important formulas of Differentiation.

d 𝓍 n / d𝓍
= n 𝓍 n-1
d (Sin𝓍) / d𝓍
= Cos𝓍
d (Cos𝓍) / d𝓍
= - Sin𝓍
d (Tan𝓍) / d𝓍
= Sec 2𝓍
d (Cot𝓍) / d𝓍
= - Cosec 2𝓍
d (Sec𝓍) / d𝓍
= Sec𝓍 ∙ Tan𝓍
d (Cosec𝓍) / d𝓍
= - Cosec𝓍 ∙ Cot𝓍
d (Sin - 1𝓍) / d𝓍
=
1 / 1 - 𝓍 2
d (Cos - 1𝓍) / d𝓍
=
- 1 / 1 - 𝓍 2
d (Tan - 1𝓍) / d𝓍
=
1 / 1 + 𝓍 2
d (Cot - 1𝓍) / d𝓍
=
- 1 / 1 + 𝓍 2
d (Sec - 1𝓍) / d𝓍
=
1 / 𝓍𝓍 2 - 1
d (Cosec - 1𝓍) / d𝓍
=
- 1 / 𝓍𝓍 2 - 1
d e 𝓍 / d𝓍
= e 𝓍
d e - 𝓍 / d𝓍
= - e 𝓍
d log 𝓍 / d𝓍
=
1 / 𝓍
d a 𝓍 / d𝓍
= a 𝓍 log𝓍
d 𝓍 / d𝓍
=
1 / 2 𝓍

## सीमाओं का प्रसार

e𝓍 = 1 + 𝓍 +
𝓍 2 / 2!
+
𝓍 3 / 3!
+ ....
e-𝓍 = 1 - x +
𝓍 2 / 2!
-
𝓍 3 / 3!
+ ....
a𝓍 = 1 + (𝓍logea ) +
(𝓍logea )2 / 2!
+
(𝓍logea )3 / 3!
+ ....
loge(1 + 𝓍 ) = 𝓍 -
𝓍 2 / 2
+
𝓍3 / 3
- ....
loge(1 - 𝓍 ) = - 𝓍 -
𝓍 2 / 2
-
𝓍3 / 3
- ....
Sin 𝓍 = 𝓍 -
𝓍 3 / 3!
+
𝓍5 / 5!
- ....
Cos 𝓍 = 1 -
𝓍 2 / 2!
+
𝓍4 / 4!
- ....
tan 𝓍 = 𝓍 +
𝓍 3 / 3
+
2𝓍5 / 15
+ ....
(1 ± 𝓍 )n = 1 ± n𝓍 +
n(n-1) / 2!
𝓍2 ± ....
( 1 +
1 / 𝓍
)𝓍 = e ( 1 +
𝓍 / 2
+
11 / 24
𝓍2 + ...... )
Σn = 1 + 2 + 3 + .... + n = n
(n+1) / 2
Σn2 = 12 + 22 + 32 + .... + n2 = n
(n+1)(2n+1) / 6
Σn3 = 13 + 23 + 33 + .... + n3 = n
{n (n+1)}2 / 4

## सीमाओं सम्बंधित कुछ महत्वपूर्ण परिणाम

lim𝓍 → 0
Sin 𝓍 / 𝓍
= 1
lim𝓍 → 0
Cos 𝓍 = 1
lim𝓍 → 0
tan 𝓍 / 𝓍
= 1
lim𝓍 → 0
e𝓍 - 1 / 𝓍
= 1
lim𝓍 → 0
b𝓍 - 1 / 𝓍
= logeb(b≠0)
lim𝓍 → 0
loge [1+𝓍] / 𝓍
= 1
lim𝓍 → 0
[1 + 𝓍]1/𝓍 = e
lim𝓍 → ∞
[ 1 +
1 / 𝓍
]𝓍 = e
lim𝓍 → a
𝓍m - am / 𝓍 - a
= mam - 1
lim𝓍 → a
𝓍m - am / 𝓍n - an
=
m / n
am - n
lim𝓍 → 0
Sin-1𝓍 = 𝓍 +
𝓍3 / 3!
+
9𝓍5 / 5!
+ .....
lim𝓍 → 0
tan-1𝓍 = 𝓍 -
𝓍3 / 3
+
𝓍5 / 5
- .....

Tags: avkalan sutra, avkalan ka formula, avkalan formula, avkalan, samakalan avkalan formula

Free
Knowledge Hub

1. 10+2 (1st year and 2nd year ) mathematics ke liye formula ka pdf post kijie.

2. 10+2 (1st year and 2nd year ) mathematics ke liye formula ka pdf post kijie.

3. Thanks for formula

4. Very good formula

5. Best formula

6. Thanks so much

7. Thanks a lot

8. Ap example bhi digiye