Find the differential $$ d y $$ of the given function. $$ y=7 x-\sin ^{2}(x) $$ $$ d y=\square $$

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1. We are given the function
   $$
   y = 7x - \sin^2(x)
   $$
   
2. Differentiate each term with respect to $$ x $$:
   - The derivative of $$ 7x $$ is $$ 7 $$.
   - For $$-\sin^2(x)$$, use the chain rule. The derivative of $$\sin^2(x)$$ is
     $$
     \frac{d}{dx} (\sin^2(x)) = 2\sin(x)\cos(x)
     $$
     Therefore,
     $$
     \frac{d}{dx}(-\sin^2(x)) = -2\sin(x)\cos(x)
     $$
     
3. Combine the derivatives:
   $$
   \frac{dy}{dx} = 7 - 2\sin(x)\cos(x)
   $$
   
4. Notice that the double angle formula states:
   $$
   \sin(2x) = 2\sin(x)\cos(x)
   $$
   Thus, we can rewrite the derivative as:
   $$
   \frac{dy}{dx} = 7 - \sin(2x)
   $$

5. Therefore, the differential $$ dy $$ is:
   $$
   dy = \left(7 - \sin(2x)\right)dx
   $$
$$ dy = (7 - \sin(2x)) \, dx $$

Find the differential of the given function.

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