Question

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?

Answer 1

to simply this take ln on both sides

Answer 2

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

Answer 3

ln y
= arcsinx (ln tanx)

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

Oh

Answer 9

now u get it?

Answer 10

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

Answer 11

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.

Answer 12

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

Answer 13

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

Answer 14

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

Answer 15

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

Answer 16

yes am in class 12

Answer 17

why cant I use chain rule here ?

Answer 18

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

Answer 19

yes I know

Answer 20

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

Answer 21

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

Answer 22

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

Answer 23

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

Answer 24

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

Answer 25

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

Answer 26

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

Answer 27

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?

Answer 28

right

Answer 29

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

Answer 30

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

Answer 31

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

Answer 32

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

Answer 33

yes

Answer 34

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

Answer 35

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

Answer 36

yeah

Answer 37

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

Answer 38

r u in delhi??

Answer 39

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

Answer 40

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

Answer 41

ive given iit right one month back...

Answer 42

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

Answer 43

how?

Answer 44

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

Answer 45

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

Answer 46

i passed in 2011..gave iit in 2011

Answer 47

lol you are brainy

Answer 48

fine fine wrote AIEEE?

Answer 49

thanx...aakash sahib kahan gaye...

Answer 50

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

Answer 51

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

Answer 52

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

Answer 53

facebook...u in delhi?

Answer 54

yes I am in Delhi.

Answer 55

You ?

Answer 56

wt school?

Answer 57

Springdales

Answer 58

you ?

Answer 59

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

Answer 60

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

Answer 61

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

Answer 62

thanks haha :) , sure.

Answer 63

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))

Answer 64

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

Answer 65

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

Answer 66

hun?

Answer 67

Damn posted my fb profile here !

Answer 68

toldya..b careful next tym

Answer 69

r u a quizzer?

Answer 70

quizzer ?

Answer 71

what do you mean ?

Answer 72

mean do u go fr quizzes and all?

Answer 73

No , you ?

Answer 74

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

Answer 75

what request ?

Answer 76

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

Answer 77

engineering physics btech

Answer 78

Oh , which university ?

Answer 79

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

Answer 80

very nice.

Answer 81

Was IIT easy this year ?

Answer 82

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

Answer 83

yes..only i screwed up...

Answer 84

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

Answer 85

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

Answer 86

assuming you mean "narayna" the area ..

Answer 87

narayana iit academy

Answer 88

Oh

Answer 89

hav u added?

Answer 90

Oh , wait i'll add now.

Answer 91

hey

Answer 92

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

Answer 93

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

Answer 94

no..

Answer 95

No ?

Answer 96

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

Answer 97

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.

Answer 98

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...