Class CBSE Class 12 Mathematics Continuity and Differentiability Q #791
KNOWLEDGE BASED
UNDERSTAND
1 Marks 2023 MCQ SINGLE
The derivative of x²ⁿ w.r.t. x is
(A) x²ⁿ⁻¹
(B) 2x²ⁿ log x
(C) 2x²ⁿ(1+log x)
(D) 2x²ⁿ(1-log x)
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AI Tutor Explanation

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Step-by-Step Solution

Let y = x^(2n)

dy/dx = 2n * x^(2n-1)

Correct Answer: None of the options are correct. The correct derivative is 2n*x^(2n-1)

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Pedagogical Audit
Bloom's Analysis: This is an UNDERSTAND question because it requires the student to recall and apply the power rule of differentiation.
Knowledge Dimension: PROCEDURAL
Justification: The question requires the student to apply a specific procedure (differentiation using the power rule) to find the derivative.
Syllabus Audit: In the context of CBSE Class 12, this is classified as KNOWLEDGE. It tests the student's knowledge of differentiation rules.

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