Proof of Quotient Rule

The quotient rule stands as a fundamental principle in calculus, offering a systematic method for differentiating functions that are expressed as the quotient of two other functions. Derived from the basic principles of differentiation, the quotient rule provides a clear and concise approach to finding the derivative of such complex functions. Its proof, rooted in the principles of limits and algebraic manipulation, elucidates the rationale behind its formulation and underscores its applicability in solving a wide array of mathematical problems. Understanding the proof of the quotient rule is essential for mastering calculus and applying its principles effectively in various mathematical and scientific contexts.