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NDA 2010
Exam
NDA
Year
2010
Subject
Mathematics
Chapter
Differentiation

NDA 2010 · Mathematics · Differentiation

If x= (2 t) and y= ^2 t , then what is (d^2 y)/(d x^2) equal to?

If x=cos⁡(2t)x=\cos (2 t) and y=sin⁡2ty=\sin ^2 t, then what is d2ydx2\frac{d^2 y}{d x^2} equal to?

Options

  1. A0
  2. Bsin⁡(2t)\sin (2 t)
  3. C−cos⁡(2t)-\cos (2 t)
  4. D−1/2-1 / 2

Correct answer

A. 0

Step-by-step solution

x=cos⁡(2t) and y=sin⁡2t∴dxdt=−2sin⁡2t and dydt=2sin⁡t⋅cos⁡t∴dydx=2sin⁡t⋅cos⁡t−4sin⁡t⋅cos⁡t=−12∴d2ydx2=0\begin{aligned} & x=\cos ^{(2 t)} \text{ and } y=\sin ^2 t \\ & \therefore \frac{d x}{d t}=-2 \sin 2 t \text{ and } \frac{d y}{d t}=2 \sin t \cdot \cos t \\ & \therefore \frac{d y}{d x}=\frac{2 \sin t \cdot \cos t}{-4 \sin t \cdot \cos t}=-\frac{1}{2} \\ & \therefore \frac{d^2 y}{d x^2}=0\end{aligned}
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