Derivatives Find the derivative of the following functions. See Example 2 of Section 3.2 for the derivative of √x.
h(t) = t²/2 + 1

Verified step by step guidance

1. Step 1: Identify the function for which you need to find the derivative. Here, the function is \( h(t) = \frac{t^2}{2} + 1 \).
2. Step 2: Apply the power rule for derivatives. The power rule states that if \( f(t) = t^n \), then \( f'(t) = n \cdot t^{n-1} \).
3. Step 3: Differentiate the first term \( \frac{t^2}{2} \). Using the power rule, the derivative of \( t^2 \) is \( 2t \). Since it is divided by 2, the derivative becomes \( \frac{2t}{2} = t \).
4. Step 4: Differentiate the constant term \( 1 \). The derivative of a constant is always 0.
5. Step 5: Combine the derivatives of each term to find the derivative of the entire function. Thus, \( h'(t) = t + 0 = t \).