Question

Help understanding notation for second derivative:

\[\frac{d^2y}{dx^2}\]

Answer 1

I know Jerison has talked about the derivative notation a hand full of times. I also know that \[\frac{d^2y}{dx^2} = \left(\frac{d}{dx}\right) \left(\frac{dy}{dx}\right) \], I'm just not clear on exactly what is meant by the notation. Why is the x squared and not the y?

Answer 2

Isn't it because

\[(\frac{d}{dx})y\]

is the differential of 'y', where d/dx indicates the differential of 'something'.
So
\[(\frac{d}{dx})y = (\frac{dy}{dx})\]

and the second differential/derivative is then d / dx of that 'something'.
\[(\frac{d}{dx})(\frac{dy}{dx})\]
At least that is my understanding.

Answer 3

That was helpful, @jkristia. Thank you.