Method of Differentiation
Logarithmic Differentiation
IIT-JEE 2001
Grade 12
Question:
If $x^m y^n = (x + y)^{m+n}$, then $\frac{dy}{dx}$ is:
(1) $\frac{x}{y}$
(2) $\frac{y}{x}$
(3) $\frac{x + y}{x}$
(4) $\frac{x + y}{y}$
Step-by-Step Solution
Key Concept: Take logarithms of both sides first: $m \ln x + n \ln y = (m + n) \ln(x + y)$, which converts the product/power relation into a sum that is easy to differentiate implicitly.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (2)