Question

Please answer fast.. ​

Answer 1

Answer:

See explanation

Step-by-step explanation:

Given

         $y=\dfrac{x}{x+a}$

Simplify it (so that a is alone which eliminates it after differentiating)

        $\Rightarrow x+a=\dfrac{x}{y}\\\Rightarrow a=\dfrac{x}{y}-x$

Now differentiate both side w.r.t. x (so that a is eliminated)

       $\Rightarrow 0=\dfrac{y(1)-x\dfrac{dy}{dx}}{y^2}-1\\\\\Rightarrow y-x\dfrac{dy}{dx}=y^2\\\Rightarrow x\dfrac{dy}{dx}=y-y^2=y(1-y)$

Hence proved