Show me a random puzzle
 Most recent collections 


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


Show me a random puzzle
▼ show ▼

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

© Matthew Scroggs 2019