Derivatives Find the derivative of the following functions. See Example 2 of Section 3.2 for the derivative of √x.
f(s) = √s/4

Verified step by step guidance

1. Step 1: Rewrite the function f(s) = \frac{\sqrt{s}}{4} in a form that is easier to differentiate. Recall that \sqrt{s} can be expressed as s^{1/2}. Therefore, f(s) = \frac{s^{1/2}}{4}.
2. Step 2: Apply the constant multiple rule of differentiation. The constant multiple rule states that the derivative of a constant times a function is the constant times the derivative of the function. Here, the constant is \frac{1}{4}. So, we need to find the derivative of s^{1/2} and then multiply it by \frac{1}{4}.
3. Step 3: Differentiate s^{1/2} using the power rule. The power rule states that if f(x) = x^n, then f'(x) = nx^{n-1}. Applying this to s^{1/2}, we get \frac{1}{2}s^{-1/2}.
4. Step 4: Multiply the result from Step 3 by the constant \frac{1}{4} from Step 2. This gives us \frac{1}{4} \times \frac{1}{2}s^{-1/2}.
5. Step 5: Simplify the expression obtained in Step 4. Combine the constants \frac{1}{4} and \frac{1}{2} to get \frac{1}{8}. Therefore, the derivative of f(s) is \frac{1}{8}s^{-1/2}.