Stuck on Calc Question

Question

Hello! I am stuck on this problem and am maybe overthinking it. I need to find t^(4)(n) for the function t(n)=3n^(-1/3) + 2n^(5/3)

Answer 1

If I am correctly seeing your question.

It's asking for t⁽⁴⁾(n) as in the 4th derivative of t(n)

t(n) = 3n^(-1/3) + 2n^(5/3)

t'(n) = (-1/3)3n^(-4/3) + (5/3)2n^(2/3)

t''(n) = (-4/3)(-1/3)3n^(-7/3) + (2/3)(5/3)2n^(-1/3)

t'''(n) = (-7/3)(-4/3)(-1/3)3n^(-10/3) + (-1/3)(2/3)(5/3)2n^(-4/3)

t⁽⁴⁾(n) = (-10/3)(-7/3)(-4/3)(-1/3)3n^(-13/3) + (-4/3)(-1/3)(2/3)(5/3)2n^(-7/3)

I hope that is correctly answering your question.