Derivatives Find the derivative of the following functions. See Example 2 of Section 3.2 for the derivative of √x.
g(t) = 6√t

Verified step by step guidance

1. Step 1: Recognize that the function g(t) = 6√t can be rewritten using exponent notation as g(t) = 6t^{1/2}.
2. Step 2: Apply the power rule for differentiation, which states that if f(t) = t^n, then f'(t) = n*t^{n-1}.
3. Step 3: Differentiate g(t) = 6t^{1/2} using the power rule. The derivative of t^{1/2} is (1/2)t^{-1/2}.
4. Step 4: Multiply the derivative of t^{1/2} by the constant 6, resulting in g'(t) = 6 * (1/2)t^{-1/2}.
5. Step 5: Simplify the expression to find the derivative g'(t) = 3t^{-1/2}.