Question

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

• 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
$\frac{y}{x}+\frac{16x}{y}+8=16$
$\Rightarrow \frac{y}{x}+16\frac{x}{y}=8$
$\Rightarrow y^2+16x^2=8xy$
On differentiating both sides w.r.t. $x$, we get
$2y\frac{dy}{dx}+32x=8y+8x\frac{dy}{dx}$
$\Rightarrow (4x-y)\frac{dy}{dx}=4(4x-y)$
$\Rightarrow \frac{dy}{dx}=4$