| Parental Genotypes | Woman: XcXc | Man: XcY |
|---|---|---|
| Offspring Possibilities | XcXc (Color Blind) | XcY (Color Blind) |
Answer the following questions with respect to the sex determining mechanism observed in honey bee.

For the curve \( \sqrt{x} + \sqrt{y} = 1 \), find the value of \( \frac{dy}{dx} \) at the point \( \left(\frac{1}{9}, \frac{1}{9}\right) \).
Find the Derivative \( \frac{dy}{dx} \)
Given:\[ y = \cos(x^2) + \cos(2x) + \cos^2(x^2) + \cos(x^x) \]