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NDA 2021
Exam
NDA
Year
2021
Subject
Mathematics
Chapter
Differentiation

NDA 2021 · Mathematics · Differentiation

If y= x · 4 x · 8 x , then what is (1)/(y) (d y)/(d x) at x=(π)/(4)...

If y=cos⁡x⋅cos⁡4x⋅cos⁡8xy=\cos x \cdot \cos 4 x \cdot \cos 8 x, then what is 1ydydx\frac{1}{y} \frac{d y}{d x} at x=π4x=\frac{\pi}{4} equal to?

Options

  1. A-1
  2. B0
  3. C1
  4. D3

Correct answer

A. -1

Step-by-step solution

y=cos⁡x⋅cos⁡4x⋅cos⁡8xln⁡y=ln⁡(cos⁡x)+ln⁡(cos⁡4x)+ln⁡(cos⁡8x)1ydydx=−tan⁡x−4tan⁡4x−8tan⁡8x\begin{aligned} & y=\cos x \cdot \cos 4 x \cdot \cos 8 x \\ & \ln y=\ln (\cos x)+\ln (\cos 4 x)+\ln (\cos 8 x) \\ & \frac{1}{y} \frac{d y}{d x}=-\tan x-4 \tan 4 x-8 \tan 8 x \end{aligned} Put x=π41ydydx=−1−4(0)−8(0)−1x=\frac{\pi}{4}\frac{1}{y} \frac{d y}{d x}=-1-4(0)-8(0)-1
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