Mathematics

You're differentiating a composite function where $r$ depends on $\theta$ through nested operations—first a sine, then a cosine. The key is recognizing the chain rule: work from the outside in, differentiating the cosine, then multiply by the derivative of its argument $(1+\sin\theta)$. Each layer peels back to reveal the next one you need to differentiate.

You're differentiating a composite function where $r$ depends on $\theta$ through nested operations—first a sine, then a cosine. The key is recognizing the chain rule: work from the outside in, differentiating the cosine, then multiply by the derivative of its argument $(1+\sin\theta)$. Each layer peels back to reveal the next one you need to differentiate.