Maximize complicated $U$ with respect to $\theta_0$ to find $S_0$ [closed]

I would like to maximize the function $$U$$ with respect to $$\theta_0$$ in order to find $$S_0$$.

That's, I want to take derivative the function $$U$$ with respect to $$\theta_0$$ in order to find $$S_0$$.

Which program should I use in order to calculate this derivative ? because it is a bit complicated.

Thank you!

(Note: Sorry for not writing the function U directly. But, I hope it is readable.)

• I've used Maple and Mathematica. Wolfram|Alpha too. Symbolab is a nice online platform, and there are other similar ones. They all have different limitations and benefits. Nothing better than good old fashioned by-hand though as a human mind can usually find more helpful and efficient ways to rewrite and structure things. May 28 at 23:48
• Your function can be written in the form $U(\theta_0) = A \exp(B \theta_0)$ for some $A$ and $B$ that do not depend on $\theta_0$, and so $U'(\theta_0) = A B \exp(B \theta_0)$, hence $U'(\theta_0) = 0$ exactly when $A B = 0$. May 29 at 0:14
• Wow! Thank you! :) Can you please write your solution more explicitly in the answer part? How you define A and B explicitly? dear @TravisWillse
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May 29 at 0:45
• So, according to @TravisWillse, if the derivative is zero anywhere, then the function is constant. May 29 at 0:51
• I know you didn't ask about this, but "take derivative [of] the function $U$ with respect to $\theta_0$ in order to find $S_0$" doesn't quite sound right to me. I'll assume that there's some context I don't know, and you know what you're doing. But @GEdgar 's comment hints that you may not be looking at your problem quite right. May 29 at 1:30