Get Answers to all your Questions

header-bg qa

Please solve RD Sharma class 12 chapter Differentiation exercise 10.2 question 60 maths textbook solution

Answers (1)


Answer: Proved

Hint: you must know the rule of solving derivation of functions.

Given:  y=\frac{x}{x+2}

Prove : x \frac{d y}{d x}=(1-y) y


Let  y=\frac{x}{x+2}

Differentiate with respect to x and apply quotient rule

\frac{d y}{d x}=\frac{d}{d x}\left(\frac{x}{x+2}\right)

\frac{d y}{d x}=\frac{(x+2) \frac{d}{d x}(x)-x \frac{d}{d x}(x+2)}{(x+2)^{2}} \ldots \frac{d}{d x} \text { u. } v=\frac{v \frac{d u}{d x}-u \frac{d v}{d x}}{v^{2}}

\begin{aligned} &\frac{d y}{d x}=\frac{x+2-x}{(x+2)^{2}} \\\\ &\frac{d y}{d x}=\frac{x+2}{(x+2)^{2}}-\frac{x}{(x+2)^{2}} \end{aligned}

\begin{aligned} &\frac{d y}{d x}=\frac{1}{x+2}-\frac{x y^{2}}{x^{2}} \\\\ &\frac{d y}{d x}=\frac{y}{x}-\frac{y^{2}}{x} \end{aligned}

\begin{aligned} &\frac{d y}{d x}=\frac{y-y^{2}}{x} \\\\ &x \frac{d y}{d x}=y(1-y) \end{aligned}

∴ Proved


Posted by


View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support