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Now we want the half-derivative of it too!

Because of Caputo’s definition of half derivatives of functions, this does not have a closed form... It requires an integral of ((t-u)^(n-3/2))(nth derivative of sin(cos(tan(u)))du where n-1<1/2<n. We can choose n=1 so that sqrt(sqrt(t-u))*-sin(tan(u))*sec^2(u)*cos(cos(tan(u))) du is integrated. 

Conclusion, the half derivative of sin(cos(tan(t))) has no closed form.

@Trexler3241. Thanks for the explanation. Now can we apply twice the half derivative definition, and find the first order derivative, even with having to deal temporarily with the integral (combining the 2 steps somehow to get the final closed form)?

@Trexler3241. I managed to verify that D^(1/2) (D^(1/2) x) = D x.

I had help with the integral of (t/(x-t))^(1/2) dt which is not easy !

I don't think that we can bypass the two integrals with a simplification of their combined action. 

While we know the chain rule of derivatives, we can use it for a lot of derivatives..

Find the derivative of x^x.

I believe this is easier than the half derivatives.

Yes, some integrals are too difficult! Maybe evaluating them in specific points could be doable. Will try some time.

For x^x we must use the log. I will let someone else try because I just did it on paper.

Yeah. We shouldn't tell them even the first step of solving it right?

Maybe, but I'm not sure if there is someone else!

Doesn't seem like it.

I'm not sure if a lot of students know of trigonometric substitution.

As if, we find the integral of (1/(1+x^2)^2 dx.

The place where all the math nerds converge

Nah, it diverges because the population is just increasing faster and faster

This is not StackExchange (https://math.stackexchange.com), but some people love math anywhere. Near chess is even better.

Do you have some data to approximate a logistic curve?

square of something, plus one.. gives the square of something else. Tells me something!

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Can we MathJax here? $\mathbb{Z}/8)^×$