Well, yesterday while doing homework i came across the following:(adsbygoogle = window.adsbygoogle || []).push({});

y=x^(ln x) asking for dy/dx

now...it looked simple. in fact it caused me severe collisions between the desk and my head...and here's why!

First chapter: Being lazy i figured why not use the chain rule. so...

dy/dx=(Ln x)*x^[(Ln x)-1]*1/x because derivative of Ln x=1/x

let's work it out. Ln x *x^(Ln x)*x^-1 * 1/x or simply by moving x on bottom

Ln x * x^Ln (x) *x^-2

okay...that is one answer. Now...the book has a formula for exponential derivatives that looks like dy/dx (a^b)= a^b *1/[b ln(a)] * b'

i don't think i'm right so i will not post what i did next becasue i'm not sure on the formula. anyway, skipping to chapter 3:

The book suggests logaritmic differentiation ( i think they call it that)

so: Chapter 3:

y=x^ Ln x

Ln y=Ln[x^(ln x)]

Ln y= Ln (x)^2 by log properties where ln x^2= 2 ln x

getting derivative:

1/y*dy/dx= 2Ln (x) *1/x and we know y=x^ ln x

dy/dx = 2Ln x * x^-1 * x^(ln x)

this is almoust what i got in first try...but not quite it.

The second one, which i got on papaer but not with me is also very close, i think it only has one less x on the bottom, butit's not the smae thing

can someone straighten this mess for me plz?

Natural logs are always doing this to me...

i'm looking for a reason why it doesn't work...and which one is correct. I'm sure that if i try again in a different way i'll get a different answer :D

Thank you

~Robokapp

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# One more problem for me

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