Question

If $\sqrt{\frac{y}{x}}+4 \sqrt{\frac{x}{y}}=4$, then $\frac{d y}{d x}=$

• A. $xy$
• B. $x / y$
• C. $-4$
• D. $4$

Answer 1

Answer: (D)

Given, $\sqrt{\frac{y}{x}}+4 \sqrt{\frac{x}{y}}=4$
On squaring both sides, we get
$\frac{y}{x}+\frac{16 x}{y}+8=16 $
$\Rightarrow \frac{y}{x}+16 \frac{x}{y}=8 $
$\Rightarrow y^{2}+16 x^{2}=8 x y$
On differentiating both sides w.r.t. $x$, we get
$2 y \frac{d y}{d x}+32 x=8 y+8 x \frac{d y}{d x}$
$\Rightarrow (4 x-y) \frac{d y}{d x}=4(4 x-y) $
$\Rightarrow \frac{d y}{d x}=4$