21–30. Derivatives
b. Evaluate f'(a) for the given values of a.
f(t) = 1/√t; a=9, 1/4

Verified step by step guidance

1. Step 1: Identify the function f(t) = \frac{1}{\sqrt{t}} and recognize that you need to find its derivative, f'(t).
2. Step 2: Rewrite the function in a form that is easier to differentiate: f(t) = t^{-1/2}.
3. Step 3: Use the power rule for differentiation, which states that if f(t) = t^n, then f'(t) = n \cdot t^{n-1}. Apply this to f(t) = t^{-1/2}.
4. Step 4: Calculate the derivative: f'(t) = -\frac{1}{2} \cdot t^{-3/2}.
5. Step 5: Evaluate f'(t) at the given values of a. First, substitute a = 9 into f'(t) to find f'(9), and then substitute a = \frac{1}{4} into f'(t) to find f'(\frac{1}{4}).