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NDA 2019
Exam
NDA
Year
2019
Subject
Mathematics
Chapter
Differentiation

NDA 2019 · Mathematics · Differentiation

If f(x)= ( x) , then f^ (x) is equal to

If f(x)=sin⁡(cos⁡x)f(x)=\sin (\cos x), then f′(x)f^{\prime}(x) is equal to

Options

  1. Acos⁡(cos⁡x)\cos (\cos x)
  2. Bsin⁡(−sin⁡x)\sin (-\sin x)
  3. C(sin⁡x)cos⁡(cos⁡x)(\sin x) \cos (\cos x)
  4. D(−sin⁡x)cos⁡(cos⁡x)(-\sin x) \cos (\cos x)

Correct answer

D. (−sin⁡x)cos⁡(cos⁡x)(-\sin x) \cos (\cos x)

Step-by-step solution

f(x)=sin⁡(cos⁡x)f′(x)=cos⁡(cos⁡x)⋅(−sin⁡x)=−sin⁡x⋅cos⁡(cos⁡x)\begin{aligned} & \quad f(x)=\sin (\cos x) \\ & f^{\prime}(x)=\cos (\cos x) \cdot(-\sin x) \\ & =-\sin x \cdot \cos (\cos x)\end{aligned}
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