Discussion Forum

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

Answer:

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