Class CBSE Class 12 Mathematics Derivatives Q #604
KNOWLEDGE BASED
UNDERSTAND
1 Marks 2024 AISSCE(Board Exam) MCQ SINGLE
The derivative of \(\tan^{-1}(x^{2})\) w.r.t. x is :
(A) \(\frac{x}{1+x^{4}}\)
(B) \(\frac{2x}{1+x^{4}}\)
(C) \(-\frac{2x}{1+x^{4}}\)
(D) \(\frac{1}{1+x^{4}}\)
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Correct Answer: B

AI Tutor Explanation

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Step-by-Step Solution

Let \(y = \tan^{-1}(x^2)\).

We need to find \(\frac{dy}{dx}\).

Using the chain rule, we have: \(\frac{dy}{dx} = \frac{d}{dx} (\tan^{-1}(x^2)) = \frac{1}{1 + (x^2)^2} \cdot \frac{d}{dx}(x^2)\)

Now, \(\frac{d}{dx}(x^2) = 2x\).

So, \(\frac{dy}{dx} = \frac{1}{1 + x^4} \cdot 2x = \frac{2x}{1 + x^4}\).

Correct Answer: \(\frac{2x}{1+x^{4}}\)

AI Suggestion: Option B

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Pedagogical Audit
Bloom's Analysis: This is an UNDERSTAND question because it requires the student to recall the derivative of the inverse tangent function and apply the chain rule.
Knowledge Dimension: CONCEPTUAL
Justification: The question tests the understanding of the concept of derivatives of inverse trigonometric functions and the application of the chain rule.
Syllabus Audit: In the context of CBSE Class 12, this is classified as KNOWLEDGE. The question directly assesses the student's knowledge of differentiation rules as covered in the textbook.

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