I am working some older final exams for my calc 1 class at university. There are several "find the derivative" questions, and while I am normally quite good at these, I got the wrong answer on one, according to wolfram alpha.

I applied exponential derivative rules to this $(3x^2+5)^{\arctan{x}}$ but that doesn't give a correct result. It is only one question of this type and was on a final exam from years ago, so we are unlikely to get a similar one on our final.

Someone asked me to provide the exponential derivative rule, so this is what I mean:
$f' a^u = a^u\*lna\*u'$

Nevertheless, I would like to know how it's done. Please kindly provide a step by step and explain the template for finding the derivative of $f(x)^{g(x)}$

Thank you.