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NDA 2010
Exam
NDA
Year
2010
Subject
Mathematics
Chapter
Differentiation

NDA 2010 · Mathematics · Differentiation

If x + y = 2 , then what is (d y)/(d x) at y=1 equal to?

If x+y=\sqrt{x}+\sqrt{y}=2,thenwhatisdydx, then what is \frac{d y}{d x} at y=1y=1 equal to?

Options

  1. A5
  2. B2
  3. C4
  4. D-1

Correct answer

D. -1

Step-by-step solution

x+y=2∴12x+12ydydx=0\begin{aligned} & \sqrt{x}+\sqrt{y}=2 \\ & \therefore \frac{1}{2 \sqrt{x}}+\frac{1}{2 \sqrt{y}} \frac{d y}{d x}=0\end{aligned}\frac{d y}{d x}=-\frac{1}{\sqrt{x}} \times \frac{\sqrt{y}}{1} \quad\left[ at y=1x+1=2x=1\begin{array}{l}\text{ at } y=1 \\ \sqrt{x}+1=2 \\ \sqrt{x}=1\end{array}\right.(dydx)y=1=−11×1=−1\begin{aligned} & \left(\frac{d y}{d x}\right)_{y=1}=-\frac{1}{1} \times 1 \\ & =-1\end{aligned}$
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