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# 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

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.

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