IIT JEE , AIEEE Forum - Mathematics , Differential Calculus

jic

the differentiation of log|x| is 1/|x| or 1/x pls explain

ganesha1991

logIxI

when x is positive
y = logx
therefore
dy/dx = 1/x

when x is negative
y = -logx
dy/dx = -1/x

combining the two answers
we get dy/dx = 1/IxI

jic

but in rd sharma objective first solved example of chapter differentiation the ans is 1/x even the option is given 1/|x|

eistien

hey when you differentiate Log|x| it

gives

I/|x|*(|x|/x) see pply chain rule no then you get the answer as 1/x

hope you understand!!!

eistien

hey ganesh i found the mistake when x is negative f(x)=log(x) and not -log(x)!!!

|-x|=x only

did you understand your mistake??

neeraj_agarwal_1990

derivative of |f(x)| is f'(x) .|f(x)|/f(x) ...

which means that for derivative of log|x| = 1/|x| .d|x|/dx (using chain rule)

also derivative of |x| by above formula is |x|/x...

so answer is 1/x

dheer_07

cummon guys how can we simply differentiate mod x???????

neeraj_agarwal_1990

making cases for f(x)>0 and f(x)<0, we can get the general formula that i have written above....

iitaspirant10

@ dheer

f(x)= |x|

dy/dx=       1 ,when x>0
                0, when x=0
         -1, when x<0

dheer_07

dats wat i wana say yaar we ve to take case rather apply chail rule!!!

eistien

so what do you all finally say isnt the answer 1/x and whats wrong with my approach

and anyone who says chain rule is wrong

it is right here as x can never take a value 0 so need not to split and you forgot that |x| in that denominator it cancels |x| in the numerator and we get the answer even if you do it by taking it case by case you will end up with the same answer!!!

answer is 1/x

eistien

hey dude here X can take any value my friend as we have Log|x| and not logx and thus even for negative values the function exists

as

f(-2)=f(2)=log(2)

i hope you understand hemant.cacr

shaan2007ster

d(log|x|)/dx

Case I. If x >0; |x| = x;

So d(logx)/dx = 1/x.

Case II. If x <0; |x| = -x;

So d(log(-x))/dx = 1/(-x) * d(-x)/dx

= 1/x;

So Ans is 1/x.

eistien

yeah you are rite i did the same way da!!! lets see where has JIC gone???

SCIENTIST135

APPLY CHAIN RULE.
d(log IxI) / dx = (1/ IxI).d (IxI) / dx
NOW DIFFERENTIATION OF IxI is IxI / x. HOPE NOW ITS CLEAR THAT ANS IS 1/x only . THIS QUES IS GIVEN IN BOTH RD AND ARIHANT DIFFERENTIAL CALCULUS

Ask & Discuss Questions with Community & Experts