mscroggs.co.uk
mscroggs.co.uk

subscribe

Puzzles

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
$$\frac{d}{dy}\left(\frac{dy}{dx}\right)$$
when:
(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

Archive

Show me a random puzzle
 Most recent collections 

Advent calendar 2023

Advent calendar 2022

Advent calendar 2021

Advent calendar 2020


List of all puzzles

Tags

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

Archive

Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2012–2024