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        riddles >> easy >> Differentiation Problem
        
(Message started by: THUDandBLUNDER on Dec 3^rd, 2003, 11:23pm)

Title: Differentiation Problem
Post by THUDandBLUNDER on Dec 3^rd, 2003, 11:23pm

Let
z = x^x
and y = x^z

Find dy/dx

Title: Re: Differentiation Problem
Post by TenaliRaman on Dec 4^th, 2003, 1:43am

::[hide]
isn't the simple chain differentiation stuff? or is there anything intricate i am missing.
y=x^z
lny=zlnx
(1/y)(dy/dx)=z/x + lnx(dz/dx) ..(*)

z = x^x
lnz = xlnx
(1/z)(dz/dx) = 1+ln(x) .. (**)

subbing (**) in (*) and rearranging,
(dy/dx) = x^{x^x+x}*(lnx)² + x^{x^x+x}*(lnx) + x^{x^x+x-1}
[/hide]::

Title: Re: Differentiation Problem
Post by towr on Dec 4^th, 2003, 2:22am

yep.. that seem about right..

this also work
::[hide]
(d/dx x^a^a + a^x^a + a^a^x)[a:=x]
[/hide]::
It probably gives some people the wrong idea though..