Different results for derivative of a function

Questions
1

Hi! My friend asked me to help to check if the derrivative of equation 9 is like equation 10. I don’t really how to solve it manually so I try to check from a couple of app and use software, but the result is different. Can you help me to check and explain if the derrivative is actually correct.

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I try with wolfram mathematica web :

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wolfram mathematica software :

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Open in Wolfram Cloud ↗

I also try to use derrivative calculator on internet (i change theta to x in this app) :

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2
Open in Wolfram Cloud ↗
3

You misunderstand the text. Equation (9) defines a function TC. Equation (10) is not the derivative of TC. It is the value of theta that makes the derivative of TC equal to zero. Mariusz has shown that the result is correct.

4

Thank you so much for the correction!

5

Right, it seems like I misunderstood the text. Thank you for explaining it to me.