derivative of x^x^x^x^x^x^x^x... as the power increases to infinitive

5 answers

y = x^x^x^...
lny = x^x^x^... lnx = y lnx
lny/y = lnx
Now differentiating implicitly,

1/y y' - lny/y^2 y' = 1/x
y' = (1/xy)/(1 - lny/y)
You can massage that in various ways.
The first five square numbers are 1, 4, 9, 16, and 25, and their average is 11. What is the average of the next five square numbers?
well, just add 'em up and divide by 5. The numbers are

36,49,64,81,100
A jug contains 1
2 L of water.
The water is shared equally among 5 children.
How much water does each child receive?
A 1
10 L
B 1
5 L
C 2
5 L
D 5
2 L
2L/5child = 2/5 L/child