Why does d/dx (dy/dx)² give 2(d²y/dx²) and not 2(dy/dx)(d²y/dx²)?

[Mgarrettny]

Can someone help me out with what I believe who.d be a straight chain rule application?

D/dx (dy/dx)^2

I would think, applying the chain rule, you get

2 (dy/dx) d/dx (dy/dx) = 2 (dy/dx) (d2y/dx2)

But, from the papers I checked, the (dy/dx) in the answer goes away, leaving just

2 (d2y/dx2)

What am I missing?

 

[Byron Chen]

Can you rewrite your question in LaTex? I don't quite follow what you are saying.

 

[arildno]

Can someone help me out with what I believe who.d be a straight chain rule application?

D/dx (dy/dx)^2

I would think, applying the chain rule, you get

2 (dy/dx) d/dx (dy/dx) = 2 (dy/dx) (d2y/dx2)

But, from the papers I checked, the (dy/dx) in the answer goes away, leaving just

2 (d2y/dx2)

What am I missing?

If you have referred correctly to the paper, the paper is wrong.

 

[Mgarrettny]

Sorry everyone, ignore this.

 

[Mgarrettny]

Thanks arildo, especially for the light speed reply. The paper was right, it was I who was wrong. I did not realize the paper was differentiating by y not x. Mea culpa.