Click here to win prizes by solving the puzzle Advent calendar.
Click here to win prizes by solving the puzzle Advent calendar.



x to the power of x again

Let \(y=x^{x^{x^{x^{...}}}}\) [\(x\) to the power of (\(x\) to the power of (\(x\) to the power of (\(x\) to the power of ...))) with an infinite number of \(x\)s]. What is \(\frac{dy}{dx}\)?

Show answer & extension

If you enjoyed this puzzle, check out Sunday Afternoon Maths V,
puzzles about algebra, or a random puzzle.


Show me a random puzzle
 Most recent collections 

Sunday Afternoon Maths LXVII

Coloured weights
Not Roman numerals

Advent calendar 2018

Sunday Afternoon Maths LXVI

Cryptic crossnumber #2

Sunday Afternoon Maths LXV

Cryptic crossnumber #1
Breaking Chocolate
Square and cube endings

List of all puzzles


dice christmas complex numbers spheres dodecagons floors number books time probabilty bases digits averages irreducible numbers square numbers integers scales ellipses coordinates fractions logic rectangles geometry shape factors graphs triangle numbers lines percentages proportion multiplication money cryptic crossnumbers colouring indices symmetry wordplay people maths unit fractions doubling angles cryptic clues parabolas odd numbers menace volume triangles numbers circles regular shapes sport taxicab geometry coins functions chess planes polygons arrows mean clocks ave remainders factorials crossnumbers square roots perfect numbers differentiation 3d shapes trigonometry chalkdust crossnumber probability sequences division hexagons crosswords means prime numbers algebra cards squares perimeter chocolate partitions multiples dates balancing games advent 2d shapes addition sums grids star numbers area rugby folding tube maps integration sum to infinity surds speed palindromes quadratics pascal's triangle routes calculus cube numbers shapes


Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2012–2019