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JEE Main 2011
Exam
JEE Main
Year
2011
Subject
Mathematics
Chapter
Differentiation

JEE Main 2011 · Mathematics · Differentiation

(d^2 x)/(d y^2) equals

d2xdy2\frac{d^2 x}{d y^2} equals

Options

  1. A−-\left(\frac{d^2 y}{d x^2}\right)^{-1}(dydx)−3\left(\frac{d y}{d x}\right)^{-3}
  2. B\left(\frac{d^2 y}{d x^2}\right)(dydx)−2\left(\frac{d y}{d x}\right)^{-2}
  3. C−-\left(\frac{d^2 y}{d x^2}\right)(dydx)−3\left(\frac{d y}{d x}\right)^{-3}
  4. D(d2ydx2)−1\left(\frac{d^2 y}{d x^2}\right)^{-1}

Correct answer

C. −-\left(\frac{d^2 y}{d x^2}\right)(dydx)−3\left(\frac{d y}{d x}\right)^{-3}

Step-by-step solution

ddy(dxdy)=ddy(1(dydx))=−1(dydx)2ddy(dydx)2\frac{d}{d y}\left(\frac{d x}{d y}\right)=\frac{d}{d y}\left(\frac{1}{\left(\frac{d y}{d x}\right)}\right)=-\frac{1}{\left(\frac{d y}{d x}\right)^2} \frac{d}{d y}\left(\frac{d y}{d x}\right)^2 =−(dydx)−21(dydx)ddx(dydx)=−(d2ydx2)(dydx)−3=-\left(\frac{d y}{d x}\right)^{-2} \frac{1}{\left(\frac{d y}{d x}\right)} \frac{d}{d x}\left(\frac{d y}{d x}\right)=-\left(\frac{d^2 y}{d x^2}\right)\left(\frac{d y}{d x}\right)^{-3}
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