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 2019

Sunday Afternoon Maths LXVII

Coloured weights
Not Roman numerals

Advent calendar 2018

Sunday Afternoon Maths LXVI

Cryptic crossnumber #2

List of all puzzles

Tags

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

Archive

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