Derivatives Of Functions In Parametric Forms

Concept: Implicit differentiation.

Step 1: Differentiate both sides.


Step 2: Apply product rule.


Step 3: Group .


Step 4: Solve for .


Step 5: Use original equation.
From given: Substitute and simplify: Conclusion:
Answer = Option (A)

Concept: Logarithmic differentiation for functions of type .

Step 1: Simplify absolute values.
At :

Step 2: Take logarithm.


Step 3: Differentiate.


Step 4: Substitute values.


Step 5: Compute derivative.
Conclusion:
Answer =