√x+√y = Ine হলে, dy/dx=? 

দেওয়া আছে, \( \sqrt{x} + \sqrt{y} = 1 \)।

উভয় পার্শে \(x\) এর সাপেক্ষে অন্তরীকরণ করে পাই,

\(\frac{d}{dx}(\sqrt{x} + \sqrt{y}) = \frac{d}{dx}(1)\)

\(\Rightarrow \frac{d}{dx}(\sqrt{x}) + \frac{d}{dx}(\sqrt{y}) = 0\)

\(\Rightarrow \frac{1}{2\sqrt{x}} + \frac{1}{2\sqrt{y}} \cdot \frac{dy}{dx} = 0\)

\(\Rightarrow \frac{1}{2\sqrt{y}} \cdot \frac{dy}{dx} = -\frac{1}{2\sqrt{x}}\)

\(\Rightarrow \frac{dy}{dx} = -\frac{2\sqrt{y}}{2\sqrt{x}}\)

\(\Rightarrow \frac{dy}{dx} = -\frac{\sqrt{y}}{\sqrt{x}}\)

\(\therefore \frac{dy}{dx} = -\sqrt{\frac{y}{x}}\) ✅