information:extraction, structural:scholar_edition, stylistic:style_transfer, information:classification, structural:summarization
Example 1

Consider

This equation is easy to solve for y, giving

where the right side is the explicit form of the function y (x). Differentiation then gives dy / dx = −1.

Alternatively, one can totally differentiate the original equation:

Solving for dy / dx gives

the same answer as obtained previously.