Need help on a fundamental theorem of calculus problem

What exactly is your question? You have correctly used the fundamental theorem to find the first derivative. The problem asks for the second derivative so differentiate again.
 
What do you mean by taking the second derivative? Do I let f(t) = f(x), and then take the second derivative? Am I allowed to do that?
 
Normally, you learn "function notation" well before starting Calculus- maybe it's been too long! If f(t)= t^3- 3t, then f(x)=x^3-3x.

You are told that
f(t)= \int_1^{t^2} \frac{\sqrt{1+u^4}{u}du
so
f(x)= \int_1^{x^2}\frac{\sqrt{1+ u^4}{u}du

Use the "Fundamental Theorem of Calculus" to differentiate that.
 
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