Final answer:
To find the second derivative of the function g(t) = t²(8t⁵)⁴, use the chain rule and power rule.
Step-by-step explanation:
To find the second derivative of the function g(t) = t²(8t⁵)⁴, we need to apply the chain rule and the power rule. Let's break it down step by step:
- Start by finding the first derivative: g'(t) = 2t(8t⁵)⁴ + t²(4)(8t⁵)³(40t⁴)
- Simplify the expression: g'(t) = 2t(8t⁵)⁴ + 4t²(8t⁵)³(40t⁴)
- Now, find the second derivative by applying the chain rule and power rule again: g''(t) = 2(8t⁵)⁴ + 2t(4)(8t⁵)³(40t⁴) + 4t²(8t⁵)³(40t⁴) + t²(4)(8t⁵)³(120t³)
- Simplify the expression further for the final answer.