Question

find dy/dx y=sqrt x raised to root x raised again to root x until infinity find dy/dx y=sqrt x raised to root x raised again to root x until infinity @Mathematics

Answer 1

help

Answer 2

\[\huge\frac{d}{dx}\sqrt{x}^{\sqrt{x}^{\sqrt{x}^{...}}}\]
is that what you are asking?

Answer 3

ya

Answer 4

pls help its urgent

Answer 5

I wrote you an answer to this yesterday I think.

Answer 6

i didnt get full answer :(

Answer 7

i am stuck

Answer 8

y=root x^y

Answer 9

log y =y log root x

Answer 10

now wat?

Answer 11

Here it is again: Let \( y = f(x) = \sqrt{x}^ {...} = \sqrt{x}^{y} \)

then \( \ln y = y. \ln (\sqrt{x}) = 1/2 . y . \ln x \)
hence
y'/y = 1/2 ( y/x + y' ln x)

Answer 12

.........urgent

Answer 13

Now solve algebraically for y'.

Answer 14

how did 1/2 yog came?

Answer 15

sqrt(x) = x^1/2 hence ln ( sqrt(x)) = 1/2 . ln x

Answer 16

because ln(a^b) = b . ln a

Answer 17

then what is answer?

Answer 18

pls help its urgent i hav no time

Answer 19

c'mon. You can solve this equation for y' :
y'/y = 1/2 ( y/x + y' ln x)

Answer 20

hence y' (1/y - ln x) = y/(2x) and therefore y' = ...

Answer 21

k how did y'/y came?

Answer 22

Implicit differentiation: (d/dx) ln y = dy/dx . 1/y

Answer 23

thx help at this too
f y= [2/(sqrt a^2-b^2)] x tan inverse [sqrt (a-b/a+b)]tan 1/2 x] then show that dy/dx=1/(a+bcosx)

Answer 24

..........

Answer 25

This one is just a messy calculation. If you know how to differentiate tan x and arctan x, then you should know how to do this.

Also you need to know that 1 + tan^2 a = sec^2 a

Answer 26

and the chain rule of course.

Answer 27

plz hlp someone adviced me trigonometric substitution pls help its urgent

Answer 28

No, trig substitution is not the answer.
Let A = [2/(sqrt a^2-b^2)] and B = sqrt (a-b/a+b)

Then you want the derivative of

y = A arctan(B tan (x/2))

Write y = A arctan u, where u = B tan(x/2)

Then \[ \frac{dy}{dx} = \frac{dy}{du}\frac{du}{dx} = \frac{A}{1+u^2} \ . \ B/2.\ \sec^2( x/2) \]

Answer 29

Now substitute back in for A, B and u and carefully calculate.

Answer 30

plz do it its urgent plssssssss

Answer 31

helo