Why does the below step result in a chain rule?
Intuitively, I would just differentiate it against y and x resulting in $-y^{-2} = -\sin{x}$.

[Khan Acad](https://www.khanacademy.org/math/ap-calculus-ab/ab-diff-contextual-applications-new/ab-4-4/v/differentiating-related-functions) mentioned something about relating y = y(t) and x = x(t), but my brain is struggling to comprehend why it can just be related like this... (Though I could just be getting it completely wrong)

[![enter image description here](https://i.stack.imgur.com/Af5Au.png)](https://i.stack.imgur.com/Af5Au.png)