Calculus

We are given: Using the chain rule: Let . Then: So: But notice: This simplifies to: But none of the options contain this expression — only (A) is a partial derivative rule form. However, since: So the correct answer isn't just (A) — it should be the full expression. Correction: The correct answer based on derivative computation is: But none of the given options match this. So either the options are incorrect or incomplete.

We differentiate term-by-term: Adding both:

We are given: Use the identity: So: Now differentiate: the question asks for: But let’s double-check the identity: Let’s write numerator and denominator in terms of half-angle identities: So yes, confirmed: So the correct answer is (C) Fixing the answer:
Correct Answer Correct Answer: (C)