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 differentiation, or a random puzzle.


Show me a random puzzle
 Most recent collections 

Advent calendar 2019

Sunday Afternoon Maths LXVII

Coloured weights
Not Roman numerals

Advent calendar 2018

Sunday Afternoon Maths LXVI

Cryptic crossnumber #2

List of all puzzles


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


Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2012–2020