I have the very basic of the chain rule understood however the functions

with powers that contain equation confuse the hell out of me I hope to get some prompt and excellent health let me show an example

$\displaystyle f(x)=e^{(1+3t)^{2}}$

and the chain rule is

$\displaystyle

f\prime(g(x)) * g\prime(x)

$

and the answer i was shown and the stops shown dont make sense from what i think i understand

$\displaystyle f\prime(x)=(e^{1+3t^{2}})(2)(1+3x)3$

I can understand $\displaystyle f\prime(x)=(e^{1+3t^{2}})$ to

$\displaystyle f\prime(g(x))$ and $\displaystyle (2)(1+3x)$ to be $\displaystyle g\prime$ however why would you derive $\displaystyle (1+3x)$ as you did all steps of the chain rule why would you need a further derivation

pretty much anything to power containing a constant confuses me

hope this posts get a reply unlike my other ones