Final answer:
The derivative of the function 2/3 * 9t² + t with respect to time t is 12t + 2/3.
Step-by-step explanation:
To find the derivative of the given function 2/3 × 9t² + t, we apply the rules of differentiation. Since we are differentiating with respect to time t, we treat t as our variable and any constant multiplier as just that, a constant that will remain through the derivative process. We can distribute the 2/3 across the terms inside the parentheses.
The derivative of t² with respect to t is 2t, and the derivative of t with respect to t is 1. Remembering to multiply by the constant 2/3 throughout, we get:
- The derivative of 2/3 × 9t² is 2/3 × 18t = 12t.
- The derivative of 2/3 × t is 2/3 × 1 = 2/3.
Therefore, the derivative of the function 2/3 × 9t² + t is 12t + 2/3.