For the curve `sqrt(x)+sqrt(y)=1` , `(dy)/(dx)` at `(1//4,\ 1//4)` is (a)`1//2` (b) 1 (c) -1 (d) 2

Explanation

To find \(\frac{dy}{dx}\) for the curve \(\sqrt{x} + \sqrt{y} = 1\) at the point \(\left(\frac{1}{4}, \frac{1}{4}\right)\), we will differentiate both sides of the equation with respect to \(x\).

### Step 1: Differentiate both sides
Starting with the equation:
\[ \sqrt{x} + \sqrt{y} = 1 \]
We differentiate both sides with respect to \(x\):
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