Find the second derivative of the function g(t) = t²(8t⁵)⁴.

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asked Oct 22, 2024 127k views

1 Answer

JonoCoetzee · Answer 1 · 2024-10-26T01:59:43+0000

To find the second derivative of the function g(t) = t²(8t⁵)⁴, use the chain rule and power rule.

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.