Differentiation

This is a parametric differentiation problem. We will find and first.
Step 1: Find .
Using the quotient rule: Step 2: Find .
. Using the quotient rule: Step 3: Find . Step 4: Evaluate the right-hand side. Since and both simplify to the same expression in terms of , we have shown that .

Concept: Use the derivative formula: Also use the identity: This simplifies the expression significantly.
Step 1: Let Using identity: So,
Step 2: Simplify inverse cosine
Step 3: Differentiate Final Answer: Explanation: Recognizing the trigonometric identity avoids complicated differentiation and makes the problem straightforward.