The following gives an answer that includes a fraction over a fraction: CAS.diff(ATAN(x/50))) gives 1/(1+(x/50)^2)/50.
I know the actual answer simplifies to 50/((x^2)+2500), however if read the wrong way as (1)/((1+(x/50)^2)/50) for example, the answer would be interpreted the wrong way. How do I tell which is the numerator and denominator?
(1) Following the "order of operations" rules, divisions always proceed left to right unless parentheses indicate otherwise. Therefore 1/2/3 always means (1/2)/3, and it NEVER means 1/(2/3). This can be seen by typing both of the latter expressions (with parentheses) into the CAS and looking at how they are displayed in the history. With Entry mode (Home Settings, page 1) set to Algebraic, and Textbook Display mode (Home Settings, page 2) turned off, typing (1/2)/3 is displayed in history as 1/2/3 because the parentheses are not needed, following the left-to-right order of operations. But typing 1/(2/3) is displayed in history as 1/(2/3) because the parentheses are needed to override the left-to-right order of operations.
(2) Just turn on Textbook Display mode (Home Settings, page 2). The precedence of the divisions is indicated by their length. Try both of the above examples and look carefully at the lengths of the division lines. The smallest ones have the highest priority, which is the universal standard for printing compound fractions.
Therefore, whether Textbook Display is on or off, multiple divisions are never ambiguous.
Hope this helps! Disclaimer: I don't work for HP. I'm just another happy HP calculator user.