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NDA 2010
Exam
NDA
Year
2010
Subject
Mathematics
Chapter
Differentiation

NDA 2010 · Mathematics · Differentiation

If x=k(θ+ θ) and y=k(1+ θ) , then what is the derivative of y with...

If x=k(θ+sin⁡θ)x=k(\theta+\sin \theta) and y=k(1+cos⁡θ)y=k(1+\cos \theta), then what is the derivative of yy with respect to xx at θ=π/2\theta=\pi / 2 ?

Options

  1. A-1
  2. B0
  3. C1
  4. D2

Correct answer

A. -1

Step-by-step solution

x=k(θ+sin⁡θ)y=k(1+cos⁡θ)⇒dxdθ=k(1+cos⁡θ)⇒dydθ=k(0−sin⁡θ)∴dydx=−sin⁡θ1+cos⁡θ=−sin⁡π21+cos⁡π2=−11=−1\begin{aligned} x & =k(\theta+\sin \theta) \\ y & =k(1+\cos \theta) \\ \Rightarrow \quad \frac{d x}{d \theta} & =k(1+\cos \theta) \\ \Rightarrow \quad \frac{d y}{d \theta} & =k(0-\sin \theta) \\ \therefore \quad \frac{d y}{d x} & =\frac{-\sin \theta}{1+\cos \theta} \\ & =\frac{-\sin \frac{\pi}{2}}{1+\cos \frac{\pi}{2}} \\ & =\frac{-1}{1}=-1\end{aligned}
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