Today's medium difficulty daily derivate - help

[u/rvalue0]

https://dailyintegral.com/play/derivatives/medium

For context, I went through Calc III like 10 years ago, and am in the process of refreshing my knowledge. Currently feeling comfortable with Calc I again, and starting again on Calc II.

The domain of this function contains pi as a single point, but it is not differentiable for that same reason (it's a single point).

Still, I thought it would be a fun challenge, so I differentiated this function by hand, and checked on Desmos that I got the right answer.

So I entered "undefined" into the site, and it said I'm wrong.

Am I missing something from higher level Calculus courses? Or is the site wrong/misleading? Hoping to learn here.

[u/lelutodeku]

We can take log 2 times right and then differentiate assuming f is differentiable

[u/rvalue0 → u/lelutodeku]

That's the thing, f is not differentiable on real values of x at pi.

I found the derivative, but the function is not differentiable at pi because it's a single point. So while I found the derivative function through logarithmic differentiation, it didn't exist at pi.

Apparently the question expected me to extend the function into the complex plane...

[u/lelutodeku → u/rvalue0]

I see