Quotient Plus Chain Rule: Worked Example and Solution

Problem 1: Differentiate $y=\frac{\ln x}{x^2}$.

Answer: $y'=\frac{1-2\ln x}{x^3}$

Why this method: quotient plus chain matches the mathematical structure before any algebraic cleanup.

1. Apply the quotient plus chain structure before simplifying.
2. Retain every factor contributed by an inner derivative.
3. A factored final form is $\frac{1-2\ln x}{x^3}$.
4. Therefore the result is $y'=\frac{1-2\ln x}{x^3}$.