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NDA 2012
Exam
NDA
Year
2012
Subject
Mathematics
Chapter
Differentiation

NDA 2012 · Mathematics · Differentiation

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

If y=cos⁡ty=\cos t and x=sin⁡tx=\sin t, then what is dydx\frac{d y}{d x} equal to?

Options

  1. Axyx y
  2. Bx/yx / y
  3. C−y/x-y / x
  4. D−x/y-x / y

Correct answer

D. −x/y-x / y

Step-by-step solution

dydt=−sin⁡t,dxdt=cos⁡tdydx=dy/dtdx/dt=−sin⁡tcos⁡t=−xy\frac{d y}{d t}=-\sin t, \frac{d x}{d t}=\cos t\frac{d y}{d x}=\frac{d y / d t}{d x / d t}=\frac{-\sin t}{\cos t}=-\frac{x}{y}.
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