Need help finding the tangent to an integral function at x=2

[plush dawn]

I'm currently stuck on a calculus problem and would greatly appreciate any help or guidance on how to proceed.

The problem is as follows: I need to find the equation of the tangent line to the function $f(x)=\int_{4}^{x^{2}} \ln \left(t^{3}+4\right) d t$ at the point where $x=2$. I've been struggling with this for a while now and can't seem to figure out how to get started.

Does anyone have any tips or suggestions for how to approach this problem? Any help would be greatly appreciated.

Thank you in advance!

[plush dawn]

I know that to find the equation of the tangent line to the function $f(x)=\int_{4}^{x^{2}} \ln \left(t^{3}+4\right) dt$ at the point where $x=2$, we can use the fundamental theorem of calculus, which states that if $f(x) = \int_a^x g(t) dt$ for some continuous function $g(t)$, then $f'(x) = g(x)$. But how do I proceed from here?

[rain leaf]

dgh

[high robin]

@plush dawn u still need help?

[plush dawn]

Yes

[limber finch]

Well for a start, you will need the FTC but also note that it's x^2 instead of x as the "top limit" (you will need the chain rule for that)