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

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

Solution:

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

 

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