Question

Derivative help!

Answer 1

\[\large If ~ y=\log[x+\sqrt{x^2+a^2}],show~that~(x^2+a^2) \times \frac{d^2y}{dx^2}+x \frac{dy}{dx}=0\]

Answer 2

\[\large \frac{dy}{dx}= \frac{1}{x+\sqrt{x^2+a^2}} \times 1 + \frac{1}{2 \sqrt{x^2+a^2}} \times 2x\]

Answer 3

am i correct till here? :|

Answer 4

@shubhamsrg

Answer 5

yesh! \m/

Answer 6

:")

Answer 7

do I need further simplification? to continue?

Answer 8

you need to find d2y/dx^2 also

Answer 9

I know,but asking do I need to simplify this more so that 2nd derivative finding becomes easier?

Answer 10

why don't you, convert the eqn in another form first ?
bring "e" into play :)

Answer 11

log?

Answer 12

e?

Answer 13

=> e^y = x+ sqrt(x^2 + a^2)

Answer 14

dahell :O aisa bhi kuch hota hai? [[ohcrap.meme]]

Answer 15

this is basically by the definition of log -_-

kya log padhe ho? :|

Answer 16

ghanta padaya tumne :/

Answer 17

hmm, sorry :/

Answer 18

achaar daalu sorry ka?

Answer 19

okay :)

Answer 20

kya karun ab?

Answer 21

aachar dalo :)
fir taste karwana..

Answer 22

neither you have time nor me so :P
bi tch please.

Answer 23

where are the mods? this guy just abused me! :O

Answer 24

e^y = x+ sqrt(x^2 + a^2)

use this to find dy/dx and d2y/dx^2

Answer 25

\[\large \frac{dy}{dx}= \frac{1}{e^y} \times 1 + \frac{1}{2 \sqrt{x^2+a^2}} \times 2x\]

Answer 26

??

Answer 27

e^y LHS me hi rakho
waise to sahi hai :')

Answer 28

idk what u r saying :P

Answer 29

anyway

Answer 30

\[\LARGE \frac{d^2y}{dx^2}=e^y+2x \times 2 \times 2 \times \sqrt{x^2+a^2} ~~ 2x\]

Answer 31

??

Answer 32

@shubhamsrg

Answer 33

well I think both methods are easy... I can do it in both ways which way you need @DLS ?

Answer 34

without e^y

Answer 35

ok :)

Answer 36

did i get the second derivative right?

Answer 37

your dy/dx is right ..well I dont see where you found second derivative for first method ?

Answer 38

well :/ okay you find,ill see

Answer 39

can you read it ?

Answer 40

can we further simplify our original dy/dx more?
http://www.wolframalpha.com/input/?i=+derivative+of+y%3D+log%28x%2B+sqrt%7Bx%5E2%2Ba%5E2%7D%29
like here

Answer 41

wait I will start again ok ?

Answer 42

okay:/