Find `(dy)/(dx)`, if ` y + siny = cosx`

Explanation

To find \(\frac{dy}{dx}\) for the equation \(y + \sin y = \cos x\), we will differentiate both sides with respect to \(x\). Here’s the step-by-step solution:

### Step 1: Differentiate both sides
We start with the equation:
\[ y + \sin y = \cos x \]
Now, we differentiate both sides with respect to \(x\).
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