Derivatives

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FUGU

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I would be sincerely thankful if someone of you also helped me with this problem

Calculate the derivative of xx^x^x^x... ;the amount of powers being n, a number that pursues infinity.
 
FUGU said:
I would be sincerely thankful if someone of you also helped me with this problem

Calculate the derivative of xx^x^x^x... ;the amount of powers being n, a number that pursues infinity.
Click to expand...

Try logarithmic differentiation. This might help, too: let y = that expression. Then y = x^y.
 
thank you for your advice, but ,sadly , itdidnt acutally work .I'll try once more!
 
i know its something with functions composition in differentials,but dont knwo how to properly do it :D
 
FUGU said:
I would be sincerely thankful if someone of you also helped me with this problem

Calculate the derivative of xx^x^x^x... ;the amount of powers being n, a number that pursues infinity.
Click to expand...

y = x^y

ln(y) = y * ln(x)

Now continue....
 
FUGU said:
So, i posted yesterday a thread about the power tower problematic. i was wondering if some of you guys could help me to calculate its derived . I have already tried in many different ways ,but i always got stuck.Please help me with a detailed explination.
https://thatsmaths.files.wordpress.com/2013/01/powertowerlambert.pdf
Click to expand...


How can we show you how to do something if we don't know what you don't know?

Do you know the product rule for differentiation? The derivative of the natural log function?

Do you know how logarithmic differentiation works? e.g. can you find the derivative of f(x) = x^(sin(x))?

Do you know the chain rule and implicit differentiation? e.g. can you find dy/dx if you're given x+y=e^(x*y)?

Can you do algebra?

The above are requirements this problem - you would not understand the solution without them.
 
More specifically - do you know how to differentiate the following implicit expression:

y = x^y............ →............ln(y) = y * ln(x)
 
im in the eleventh grade and i have just done the basic rules to derive like (lnx)'=1/x
(xx)=xxlnx+xx and so on. i have never used this notion in any of my work "d(x)/d(y)"
 
FUGU said:
im in the eleventh grade and i have just done the basic rules to derive like (lnx)'=1/x
(xx)=xxlnx+xx and so on. i have never used this notion in any of my work "d(x)/d(y)"
Click to expand...

How did you calculate the derivative of xx - can you please show us?
 
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