MP Board · Class 11 · Mathematics · Limits and DerivativesWhat is the derivative of $f(x) = x^n$ with respect to $x$?
Step-by-Step Solution
According to the power rule of differentiation, $\frac{d}{dx}(x^n) = n x^{n-1}$.
Detailed Options Breakdown
Option : n x^n
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Limits and Derivatives.
Option 1: n x^{n-1} (Correct Answer)
Correct choice. Refer to the step-by-step verified solution guidelines above for details.
Option 2: \frac{x^{n+1}}{n+1}
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Limits and Derivatives.
Option 3: (n-1)x^n
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.