Home » Ask & Discuss » Mathematics
« Back to Discussion

Differential Calculus

New kid on the Block

Joined:	14 May 2007
Post:	6

15 May 2007 15:43:30 IST

0 People liked this

700

try this

Engineering Entrance , JEE Main , JEE Advanced , Mathematics , Differential Calculus

show that the nth derivative of (1-x²) is

n! /2( 1/(1-x)ⁿ⁺¹) + (-1)ⁿ /(1+x)ⁿ⁺¹ )

Comments (5)

$h0cK3r

Forum Expert

Joined: 27 Dec 2006

Posts: 565

15 May 2007 22:11:40 IST

Like 0 people liked this

the question is wrong it should be

nth derivative of 1/(1-x²)

let y= 1/(1-x²)

resolving the above expression in partial fractions we get

y=1/2[1/(1+x)+1/(1-x)]

now differentiating n times we get

y=n! /2( 1/(1-x)ⁿ⁺¹) + (-1)ⁿ /(1+x)ⁿ⁺¹ )

Arjun

Blazing goIITian

Joined: 12 Nov 2006

Posts: 413

15 May 2007 22:32:02 IST

Like 0 people liked this

hy shakirshafi......can u plzzzzz tell me da general formula for claculating da nth derivative

prasad rao

Blazing goIITian

Joined: 12 May 2007

Posts: 328

15 May 2007 23:06:53 IST

Like 2 people liked this

general formula of nth derivative of 1/(ax+b)^r is

(-1)^n (n+r-1)! (a)^n / (ax+b)^(n+r) (r-1)!

space indicates multiplication sign

it is a very important formula and very few people know abt it

try solving with this formula n u will make wonders

Hey I really deserve rating yaar

$h0cK3r

Forum Expert

Joined: 27 Dec 2006

Posts: 565

16 May 2007 15:19:01 IST

Like 1 people liked this

well general method i can give u a very good idea

here

suppose a function be x^m

then the nth derevative will be like this see

y=x^m

y`=mx^m-1

y``=m*(m-1)x^m-2

for the nth derevative

dⁿy/dxⁿ=m*(m-1)(m-2)(m-3)(m-4)............(m-n)x^m-n

we multiply and divide by n!

dⁿy/dxⁿ=m!/n!x^m-n

dⁿy/dxⁿ=^mP_n x^m-n

this is the method

using this we can calculate for

general formula of nth derivative of (ax+b)^-r is

(-1)ⁿ (n+r-1)! (a)ⁿ / (ax+b)^n+r (r-1)!

(as wriiten by prasad)

for such problems we need to find a relation between the derevatives!!

as a function of the number of times differenciated!!

these things dont come in JEE!!

all this successive differenciation and leibnitz theorum

i.e sucessive differenciation of product of two functions!!

Abhijat Murali

New kid on the Block

Joined: 14 May 2007

Posts: 6

19 May 2007 10:03:08 IST

Like 0 people liked this

sorry for givin a wrong question

shakirshafil gave the rite question and answer

Quick Reply

Reply

	Some HTML allowed.
	Keep your comments above the belt or risk having them deleted.
	Signup for a avatar to have your pictures show up by your comment
	If Members see a thread that violates the Posting Rules, bring it to the attention of the Moderator Team

Free Sign Up!

Preparing for JEE?

Kickstart your preparation with new improved study material - Books & Online Test Series for JEE 2014/ 2015

@ INR 4,950/-

For Quick Info

Name

Mobile

E-mail

City

Class

Find Posts by Topics

Physics

Topics

10270

20998

3866

2300

8075

2968

2788

Mathematics

Chemistry

Biology

Institutes

Parents Corner

Board

Fun Zone