hi, i was wondering if you could help me through this problem i had seen on the internet and has baffled me since. My name is michael hackman, i am a freshamn at Marshall University Here it is:

Find the derivative of: y = x^x^x^x... on to infinity.

Thanks for the help!

Hi Michael,

The key to solving this problem is to write

y = xxx ...


y = xy

Now you can differentiate implicitly in either of two ways.

Take the log of both sides
ln(y) = y ln(x)

and then differentiate with respect to x,


solve for x
x = y1/y = exp(ln(y)/y)

and then differentiate with respect to x.

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