# Sunday Afternoon Maths XXIX

**Posted on 2014-09-21**

## 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) \(y=\sin(x)\)?

## Equal opportunity

Source: Futility Closet

Can two (six-sided) dice be weighted so that the probability of each of the numbers 2, 3, ..., 12 is the same?

## Three squares

Source: Numberphile

The diagram shows three squares with diagonals drawn on and three angles labelled.

What is the value of \(\alpha+\beta+\gamma\)?

If you enjoyed these puzzles, check out Sunday Afternoon Maths LXVII,

puzzles about graphs, or a random puzzle.

puzzles about graphs, or a random puzzle.