Question

derivative of x^ln(x)

Answer 1

You can solve this question using logarithmic differentiation

Answer 2

Let,

\[\large{y = x^{\ln x}}\]

Taking log both sides:

\[\large{\implies \ln y = \ln (x^{\ln x})}\]

Answer 3

You can simplify the RHS by using this :

\[\large{\ln (a^b) = b\ln a}\]

Answer 4

Can you simplify the RHS now ?

Answer 5

ya wait

Answer 6

But first:

\[\large{\color{blue}{\text{Welcome to }}\color{red}{\text{OPENSTUDY!!}}}\]

Answer 7

;) I forgot this part ^^

Answer 8

Just take all my medals @vishweshshrimali5

Answer 9

:P Then what would happen to your 99 smart score ? O.o

Answer 10

guys i couldnt

Answer 11

Okay no problem. What part you didn't get ?

Answer 12

It's ok, I'm a selfless man.

Answer 13

?

Answer 14

:D I need many of such people ^^^ @iambatman ;)

Answer 15

Working together we can defeat satellite :P

Answer 16

is rhs= ln(x).ln(x)??

Answer 17

I can defeat him easily, :)

Answer 18

Perfect

Answer 19

Very good :)

@Miracrown I will pass on your acceptance letter of challenge to @satellite73 :)

Answer 20

Okay Sanket lets proceed

Answer 21

ya

Answer 22

You got this part:

\[\large{\ln y = \ln (x^{\ln x})}\]

\[\implies \large{\ln y = (\ln x)^2}\]

Answer 23

i got [2*ln(x)]/x

Answer 24

Is that your final answer ?

Answer 25

ya

Answer 26

How did you get that ?

Answer 27

You have missed something... Check it again

Answer 28

d(lnx.lnx)/dx

Answer 29

* in the answer

Answer 30

Okay

Answer 31

Very good.

You are correct in that part.

Answer 32

oky then whats wrong??

Answer 33

So on differentiating both sides we got this:

\[\large{\cfrac{1}{y} \ dy = \cfrac{2 \ln x}{x}}\]


Clear ?

Answer 34

ohh ya,thanks man

Answer 35

Got the answer ?

Answer 36

yup

Answer 37

Great! Congrats :D

Answer 38

thanks to u :D

Answer 39

It was my pleasure :)

And let me give you your first medal on OS for your sincere efforts

Answer 40

Enjoy the time on OS

Answer 41

ya thanks...i finally found something for my homeworks :D