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Puzzles

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) $$y=\sin(x)$$?
If you enjoyed this puzzle, check out Sunday Afternoon Maths XXIX,
puzzles about differentiation, or a random puzzle.

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