ln( ) , atan( ) functions , and derivative.

[lvl107]

Hello, Everyone.

Thanks in advance for your time and help.

Best Regards.

[Werner_E]

Guess you know that F1 and F2 are equivalent expressions, their difference is zero.

Proof is easy, as the derivative is zero the diff itself has to be a constant. So evaluating the difference function at an arbitrary x yields zero.

To get Mathcad to simplify that diff to zero seems to be a hard to impossible task.

[lvl107]

Thanks for your response, Werner.

Regards.

[lvl107]

And the similar question :

Best Regards.

[AlanStevens · Accepted solution]

See attached.

Alan

[Werner_E]

I'm not sure what your c(x) should show, but it was interested to see (graphing F1 and F2 didn't came to my mind) that F1 and F2 sem to be equivalent only for x>0.

x=0 being a special case which neither fits to the positive nor the negative x values and can be simplified (only with the additional use of max) quite nice.

[lvl107]

Many thanks for your hint and help, Alan.

Loi.

[lvl107]

Hello, Everyone again.

And the related question :

Best Regards.