`"Find "(dy)/(dx)" for "y=sin(x^(2)+1).`

Explanation

To find \(\frac{dy}{dx}\) for the function \(y = \sin(x^2 + 1)\), we will use the chain rule of differentiation. Here’s a step-by-step solution:

### Step 1: Identify the outer and inner functions
In the function \(y = \sin(x^2 + 1)\), we can identify:
- The outer function: \(u = \sin(v)\) where \(v = x^2 + 1\)
- The inner function: \(v = x^2 + 1\)

### Step 2: Differentiate the outer function
...