Two tangents

Source: Reddit
Find a line which is tangent to the curve \(y=x^4-4x^3\) at 2 points.

Show answer

Double derivative

What is
(i) \(y=x\)
(ii) \(y=x^2\)
(iii) \(y=x^3\)
(iv) \(y=x^n\)
(v) \(y=e^x\)
(vi) \(y=\sin(x)\)?

Show answer & extension

Differentiate this

$$f(x)=e^{x^{ \frac{\ln{\left(\ln{x}\right)}}{ \ln{x}}} }$$
Find \(f'(x)\).

Show answer

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


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


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


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