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?

- anonymous

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- anonymous

to simply this take ln on both sides

- anonymous

\[y=\tan(x)^{\arcsin(x)}\]

- anonymous

ln y
= arcsinx (ln tanx)

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## More answers

- anonymous

What's wrong with what I said about the chain rule ?

- anonymous

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

- anonymous

like if uv got
f(x) and g(x)
and y=f^g
dy/dx = gf^(g-1) + (lnf)f^g

- anonymous

Getting confused. Dont understand why I need to add functions here.

- anonymous

Oh

- anonymous

now u get it?

- anonymous

dy/dx = gf^(g-1) + (lnf)f^g makes it to add ..

- anonymous

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.

- anonymous

f(x)=h(g(x)) , f'(x) = h'(g(x))*g'(x) , is this not what I did too ?

- anonymous

derivative of outside function w.r.t its argument * derivative of argument w.r.t independent variable

- anonymous

u know it right..but here we cannot use the chain rule

- anonymous

u tell me...r u in class 12?

- anonymous

yes am in class 12

- anonymous

why cant I use chain rule here ?

- anonymous

for using the chain rule for sin(e^x) do u need to know the derivative of sinx or not?

- anonymous

yes I know

- anonymous

ur thinking of simpler derivatives for the chain rule..for eg we know a^x ka derivative...so hencewe can derive a^f(x)

- anonymous

wont that be cos(e^x) * e^x ?

- anonymous

yes...just an example..the thing is that there is no standard derivative of tanx ^x

- anonymous

ur treating ur function as f(g(x)) where f is tanx and g is arcsinx which is wrong

- anonymous

yes am treating it like that , why is it wrong ??

- anonymous

agar aisa hota to it wldve been tan (arcsinx) or something

- anonymous

acha , see this , how do you differenciate x^x w.r.t x then ?

- anonymous

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?

- anonymous

right

- anonymous

so u do logarithmic differentiation or u maro style and keep one fn constant and do that pellet...right...?

- anonymous

thing is I have not yet come to logarithmic differentiation abhi tak ... all I know is chain rule

- anonymous

I can blindly convince myself that I might need logarithmic differentiation for this , but I truly dont understand why chain rule cant do.

- anonymous

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

- anonymous

yes

- anonymous

this is a chain rule question...just gotta use brains and log properties

- anonymous

is it like when g and f are 2 functions of x and h is another function = g^f , you need to use logarithmic ?

- anonymous

yeah

- anonymous

see
y = x^sinx
ln y= sinxlnx
now use chain rule

- anonymous

r u in delhi??

- anonymous

thanks a lot..u gave me something to think abt...mazaa aagaya..bt dont think m nerdy...

- anonymous

yes .. ;) lol no problems , what do you do ?

- anonymous

ive given iit right one month back...

- anonymous

hey him1618, i think chain rule can suffice ... no log needed

- anonymous

how?

- anonymous

Like you were in 12th and gave IIT or just gave IIT being elder?

- anonymous

abhi 12th pass ki hai yyar..beizzati mat karo

- anonymous

i passed in 2011..gave iit in 2011

- anonymous

lol you are brainy

- anonymous

fine fine wrote AIEEE?

- anonymous

thanx...aakash sahib kahan gaye...

- anonymous

yeah..but marks nahi lagaye..wanted to be free

- anonymous

Aakash went to temple .. will be right back soon he says.

- anonymous

Are you on any IM ? What's your gtalk ?

- anonymous

facebook...u in delhi?

- anonymous

yes I am in Delhi.

- anonymous

You ?

- anonymous

wt school?

- anonymous

Springdales

- anonymous

you ?

- anonymous

k.....add Himanish...studied at St. Columba's School

- anonymous

http://www.facebook.com/profile.php?id=100002411313746

- anonymous

ur pretty...g2g...ill add u

- anonymous

thanks haha :) , sure.

- anonymous

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))

- anonymous

we find the first one using log .. as u said

- anonymous

dont pste ur fb id on public pages....aakash....sk goyal ke phatte aise hi nhi maare..bye

- anonymous

hun?

- anonymous

Damn posted my fb profile here !

- anonymous

toldya..b careful next tym

- anonymous

r u a quizzer?

- anonymous

quizzer ?

- anonymous

what do you mean ?

- anonymous

mean do u go fr quizzes and all?

- anonymous

No , you ?

- anonymous

yeah..i am..just inquiring whether uve heard of the columban open quiz...nvm...ive sent u d request

- anonymous

what request ?

- anonymous

btw what are you planning to study next after 12th ?

- anonymous

engineering physics btech

- anonymous

Oh , which university ?

- anonymous

abhi result to aane do yaar..waise i think ill get into one of the IITs

- anonymous

very nice.

- anonymous

Was IIT easy this year ?

- anonymous

How many hours do you study for IIT ? Went to any coaching ?

- anonymous

yes..only i screwed up...

- anonymous

narayana...no defined hours of study...

- anonymous

went to any coaching classes at narayana or you stay at narayana ?

- anonymous

assuming you mean "narayna" the area ..

- anonymous

narayana iit academy

- anonymous

Oh

- anonymous

hav u added?

- anonymous

Oh , wait i'll add now.

- anonymous

hey

- anonymous

how do you get an area under a function f(x) between spans x=a and x=b when you integrate it ?

- anonymous

How come it fetches you the area ? intuition behind it ?

- anonymous

no..

- anonymous

No ?

- anonymous

u divide the area under the graph into small strips along the x-axis, each having width dx

- anonymous

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.

- anonymous

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...

- anonymous

lol

- anonymous

so dA = f(x)dx

- anonymous

now area is the summation of all these small areas

- anonymous

\[A =\lim_{dx \rightarrow 0} \sum_{a}^{b}f(x)dx = \int\limits_{b}^{a}f(x)dx\]

- anonymous

get it now?

- anonymous

u cn call me if u want...m free after monday...only if ur comfortable with it

- anonymous

samajh aaya?

- anonymous

wait reading

- anonymous

I will definitely call you on mind , if you dont mind getting disturbed.

- anonymous

*monday not mind lol

- anonymous

after monday..no disturbance frm gorgeous ppl...;)

- anonymous

ill msg my no on fb
kal dekhlena

- anonymous

;) sure. I understood the intuition somewhat now , cool. thanks

- anonymous

no prob mis...ek din derivative bhi samjhaaoonga..bye g2g

- anonymous

sure

- anonymous

bye

- anonymous

u preparing for iit?

- anonymous

Not really , I think its too late now ? I never went to any coaching or prepared with IIT point of view.

- anonymous

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

- anonymous

lol really ? well I was just trying to understand how that works.

- anonymous

Trust me yaar , am weak at maths. I dont do well at all.

- anonymous

waise india ka education system is bakwas

- anonymous

i msgd u my number

- anonymous

Alright , surely will call you Mr. Brains.

- anonymous

so wtr u doing now?

- anonymous

just browsing. YouTube.

- anonymous

You heard of Manipal ?

- anonymous

university?my pals giving the exam tomorrow

- anonymous

Yes. You dont have plans for that? I heard its good?

- anonymous

Where is it actually?

- anonymous

in the south .. good

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