NCERT · Class 11 · Mathematics · Limits and DerivativesWhat is the derivative of $\frac{u}{v}$ with respect to $x$ (Quotient Rule)?
Step-by-Step Solution
According to the quotient rule of differentiation, $\frac{d}{dx}\left(\frac{u}{v}\right) = \frac{v \frac{du}{dx} - u \frac{dv}{dx}}{v^2}$, provided $v \neq 0$.
Detailed Options Breakdown
Option : \frac{u \frac{dv}{dx} - v \frac{du}{dx}}{v^2}
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Limits and Derivatives.
Option 1: \frac{v \frac{du}{dx} - u \frac{dv}{dx}}{v^2} (Correct Answer)
Correct choice. Refer to the step-by-step verified solution guidelines above for details.
Option 2: \frac{du}{dx} + \frac{dv}{dx}
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Limits and Derivatives.
Option 3: \frac{v \frac{du}{dx} + u \frac{dv}{dx}}{v^2}
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Limits and Derivatives.
💡 Study Guide: This question tests core syllabus concepts from Limits and Derivatives. For formulas, key summaries, and mock exam reference guides, read the full Limits and Derivatives Revision Notes.