Differentiation

Step 1: Use quotient rule. where and .

Step 2: Differentiate numerator and denominator.

Step 3: Apply the quotient rule.

Step 1: Differentiate both sides of the equation with respect to . Applying implicit differentiation:

Step 2: Use the product rule and chain rule:

Step 3: Combine both expressions:

Step 4: Solve for , and simplify to get the desired result:

Step 1: Use the chain rule for differentiation. Let , so that .

Step 2: Differentiate with respect to : Thus, the derivative of is .

Step 3: Now, differentiate with respect to using the chain rule:

Step 4: Multiply the results from the previous steps: