127k views
1 vote
Find the second derivative of the function g(t) = t²(8t⁵)⁴.

User Mayu
by
8.1k points

1 Answer

4 votes

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:

  1. Start by finding the first derivative: g'(t) = 2t(8t⁵)⁴ + t²(4)(8t⁵)³(40t⁴)
  2. Simplify the expression: g'(t) = 2t(8t⁵)⁴ + 4t²(8t⁵)³(40t⁴)
  3. 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)
  4. Simplify the expression further for the final answer.

User JonoCoetzee
by
7.9k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories