Find `(dy)/(dx)` if `xsin y+ y sin x=0`

Explanation

To find \(\frac{dy}{dx}\) for the equation \(x \sin y + y \sin x = 0\), we will use implicit differentiation. Here’s the step-by-step solution:

### Step 1: Differentiate both sides with respect to \(x\)
We start with the equation:
\[ x \sin y + y \sin x = 0 \]
Differentiating both sides with respect to \(x\), we apply the product rule and chain rule where necessary.
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