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NDA 2023
Exam
NDA
Year
2023
Subject
Mathematics
Chapter
Differentiation

NDA 2023 · Mathematics · Differentiation

What is the derivative of ^2 x with respect to ^2 x ?

What is the derivative of sin⁡2x\sin ^2 x with respect to cos⁡2x\cos ^2 x ?

Options

  1. A−1-1
  2. B11
  3. Csin⁡2x\sin 2 x
  4. Dcos⁡2x\cos 2 x

Correct answer

A. −1-1

Step-by-step solution

d(sin⁡2x)d(cos⁡2x)=ddxsin⁡2xddcos⁡2x=2sin⁡xcos⁡x−2sin⁡xcos⁡x=−1\frac{d\left(\sin ^2 x\right)}{d\left(\cos ^2 x\right)}=\frac{\frac{d}{d x} \sin ^2 x}{\frac{d}{d} \cos ^2 x}=\frac{2 \sin x \cos x}{-2 \sin x \cos x}=-1
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