Question

If $y=\frac{x}{a+\frac{x}{b+y}}$, then $\frac{dy}{dx}$ is

• A. $\frac{a}{ab+2ay}$
• B. $\frac{b}{ab+2by}$
• C. $\frac{a}{ab+2by}$
• D. $\frac{b}{ab+2ay}$

Answer 1

The correct option is D $\frac{b}{ab+2ay}$

$y=\frac{x}{a+\frac{x}{b+y}}$

$y=\frac{x(b+y)}{ab+ay+x}$

$\Rightarrow$ $aby+a{y}^2+xy=xb+xy$

$\Rightarrow$ $aby+a{y}^2=xb$

Differentiating both side w.r.t $x$ we get,

$\Rightarrow ab\frac{dy}{dx}+2ay\frac{dy}{dx}=b\Rightarrow \frac{dy}{dx}=\frac{b}{ab+2ay}$