Limits

We are asked to differentiate the function: Step 1: Differentiate
For the term , we apply the chain rule: The derivative of is simply , and here we multiply by the derivative of the exponent (which is 2).
Step 2: Differentiate
The derivative of is straightforward: The derivative of is , and multiplying by the constant factor 2 gives the result.
Step 3: Combine the results
Now, we sum the derivatives of both terms: Thus, the derivative is , which simplifies to when evaluated at specific values of .

We are given the limit expression: Step 1: Evaluate the limit
This is a standard limit problem. As , the expression simplifies to:
Step 2: Differentiate the result
Once we have simplified the expression, we can differentiate it. Since we are differentiating a constant function, the derivative is 0. Thus, the answer is 0.