Answer:
Option D
Explanation:
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
$2y\frac{dy}{dx}+32x=8y+8x \frac{dy}{dx}$
$\Rightarrow$ $(4x-y) \frac{dy}{dx}=4(4x-y)\Rightarrow \frac{dy}{dx}=4$
Hence, option (d) is correct
