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NDA 2023 Maths · Mathematics · Derivatives · medium

If f(x)=x^2sin x, then f' ((π)/(2)) is equal to

Single correct option

If f(x)=x2sin⁡xf(x)=x^2\sin x, then f′ ⁣(π2)f'\!\left(\dfrac\pi2\right) is equal to
  1. A. π24\dfrac{\pi^2}4
  2. B. 2π2\pi
  3. C. π+π24\pi+\dfrac{\pi^2}4
  4. D. π\pi
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Answer: (D) π\pi

By the product rule f′(x)=2xsin⁡x+x2cos⁡xf'(x)=2x\sin x+x^2\cos x. At x=π2x=\dfrac\pi2: 2⋅π2⋅1+π24⋅0=π2\cdot\dfrac\pi2\cdot1+\dfrac{\pi^2}4\cdot0=\pi. The value π24\dfrac{\pi^2}{4} results from forgetting that cos⁡π2=0\cos\dfrac\pi2=0 kills the second term but also dropping the first.
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Original question written in the NDA 2023 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake