Question

If $y=\frac{x}{(x+5)}$, then $\frac{dx}{dy}$ equals-

• A. $\frac{5}{(1-y{)}^2}$
• B. $\frac{5}{(1+y{)}^2}$
• C. $\frac{1}{(1+y{)}^2}$
• D. None of these

Answer 1

The correct option is A $\frac{5}{(1-y{)}^2}$

Given, $y=\frac{x}{x+5}$

$\Rightarrow yx+5y=x$

$\Rightarrow x(1-y)=5y$

So, $x=\frac{5y}{1-y}$

We know,

$\frac{d}{dt}\left(\frac{u}{v}\right)$ $=\frac{u\frac{d}{dt}\left(v\right)-\left(v\right)\frac{d}{dt}\left(u\right)}{v^2}$

Therefore, $\frac{dx}{dy}=\frac{5(1-y)+5y}{{(1-y)}^2}$

$\Rightarrow \frac{dx}{dy}=\frac{5}{{(1-y)}^2}$