y=(tan(x))^arcsin(x) , whats dy/x ? Wont this be d(tan(x)^arcsin(x))/dtan(x) * d(tan(x))/dx according to the chain rule ? Where am I going wrong?

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y=(tan(x))^arcsin(x) , whats dy/x ? Wont this be d(tan(x)^arcsin(x))/dtan(x) * d(tan(x))/dx according to the chain rule ? Where am I going wrong?

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to simply this take ln on both sides
\[y=\tan(x)^{\arcsin(x)}\]
ln y = arcsinx (ln tanx)

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What's wrong with what I said about the chain rule ?
ur doing it wrong..its complicated..if u want it that way u treat one fn as constant and then diff and add it to the derivative keeping second fn constant
like if uv got f(x) and g(x) and y=f^g dy/dx = gf^(g-1) + (lnf)f^g
Getting confused. Dont understand why I need to add functions here.
Oh
now u get it?
dy/dx = gf^(g-1) + (lnf)f^g makes it to add ..
but can you tell me whats wrong with the chain rule ? am afraid I have not understood the chain rule itself properly cause of it got wrong.
f(x)=h(g(x)) , f'(x) = h'(g(x))*g'(x) , is this not what I did too ?
derivative of outside function w.r.t its argument * derivative of argument w.r.t independent variable
u know it right..but here we cannot use the chain rule
u tell me...r u in class 12?
yes am in class 12
why cant I use chain rule here ?
for using the chain rule for sin(e^x) do u need to know the derivative of sinx or not?
yes I know
ur thinking of simpler derivatives for the chain rule..for eg we know a^x ka derivative...so hencewe can derive a^f(x)
wont that be cos(e^x) * e^x ?
yes...just an example..the thing is that there is no standard derivative of tanx ^x
ur treating ur function as f(g(x)) where f is tanx and g is arcsinx which is wrong
yes am treating it like that , why is it wrong ??
agar aisa hota to it wldve been tan (arcsinx) or something
acha , see this , how do you differenciate x^x w.r.t x then ?
cz remember in a composite fn in place of X there is another function, here theres no function in place of x itself na? do u c?
right
so u do logarithmic differentiation or u maro style and keep one fn constant and do that pellet...right...?
thing is I have not yet come to logarithmic differentiation abhi tak ... all I know is chain rule
I can blindly convince myself that I might need logarithmic differentiation for this , but I truly dont understand why chain rule cant do.
this is only an extension of chain rule..bt ive taught u now havent i whenever u c exponents like y=f^g take log on both sides and then u can apply chain rule
yes
this is a chain rule question...just gotta use brains and log properties
is it like when g and f are 2 functions of x and h is another function = g^f , you need to use logarithmic ?
yeah
see y = x^sinx ln y= sinxlnx now use chain rule
r u in delhi??
thanks a lot..u gave me something to think abt...mazaa aagaya..bt dont think m nerdy...
yes .. ;) lol no problems , what do you do ?
ive given iit right one month back...
hey him1618, i think chain rule can suffice ... no log needed
how?
Like you were in 12th and gave IIT or just gave IIT being elder?
abhi 12th pass ki hai yyar..beizzati mat karo
i passed in 2011..gave iit in 2011
lol you are brainy
fine fine wrote AIEEE?
thanx...aakash sahib kahan gaye...
yeah..but marks nahi lagaye..wanted to be free
Aakash went to temple .. will be right back soon he says.
Are you on any IM ? What's your gtalk ?
facebook...u in delhi?
yes I am in Delhi.
You ?
wt school?
Springdales
you ?
k.....add Himanish...studied at St. Columba's School
http://www.facebook.com/profile.php?id=100002411313746
ur pretty...g2g...ill add u
thanks haha :) , sure.
hey him... sorry .. now i realize my mistake .. u r rite ... we need to find the derivative of x^arcsin(x) and then multiply with diff of tan (x^arcsin(x))
we find the first one using log .. as u said
dont pste ur fb id on public pages....aakash....sk goyal ke phatte aise hi nhi maare..bye
hun?
Damn posted my fb profile here !
toldya..b careful next tym
r u a quizzer?
quizzer ?
what do you mean ?
mean do u go fr quizzes and all?
No , you ?
yeah..i am..just inquiring whether uve heard of the columban open quiz...nvm...ive sent u d request
what request ?
btw what are you planning to study next after 12th ?
engineering physics btech
Oh , which university ?
abhi result to aane do yaar..waise i think ill get into one of the IITs
very nice.
Was IIT easy this year ?
How many hours do you study for IIT ? Went to any coaching ?
yes..only i screwed up...
narayana...no defined hours of study...
went to any coaching classes at narayana or you stay at narayana ?
assuming you mean "narayna" the area ..
narayana iit academy
Oh
hav u added?
Oh , wait i'll add now.
hey
how do you get an area under a function f(x) between spans x=a and x=b when you integrate it ?
How come it fetches you the area ? intuition behind it ?
no..
No ?
u divide the area under the graph into small strips along the x-axis, each having width dx
Dude , gimme an IM. I cant login to facebook right now , my sis's logged in and if I log out , she'll scream , its her laptop. Give me your google talk or msn or yahoo or AIM or skype or whatever.
these rectangular strips have height f(x) at point x, and width dx no IM now...my bits is on monday..sm1 sees m dead...
lol
so dA = f(x)dx
now area is the summation of all these small areas
\[A =\lim_{dx \rightarrow 0} \sum_{a}^{b}f(x)dx = \int\limits_{b}^{a}f(x)dx\]
get it now?
u cn call me if u want...m free after monday...only if ur comfortable with it
samajh aaya?
wait reading
I will definitely call you on mind , if you dont mind getting disturbed.
*monday not mind lol
after monday..no disturbance frm gorgeous ppl...;)
ill msg my no on fb kal dekhlena
;) sure. I understood the intuition somewhat now , cool. thanks
no prob mis...ek din derivative bhi samjhaaoonga..bye g2g
sure
bye
u preparing for iit?
Not really , I think its too late now ? I never went to any coaching or prepared with IIT point of view.
k..to yeh dabanng question kahaan se laye the?i think ur mind works in the right way..90 pc people don t even think abt d meaning f an integral
lol really ? well I was just trying to understand how that works.
Trust me yaar , am weak at maths. I dont do well at all.
waise india ka education system is bakwas
i msgd u my number
Alright , surely will call you Mr. Brains.
so wtr u doing now?
just browsing. YouTube.
You heard of Manipal ?
university?my pals giving the exam tomorrow
Yes. You dont have plans for that? I heard its good?
Where is it actually?
in the south .. good

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