An amusing derivative.

June 13 2012 jaytreiman 221


On a calculus 2 test I was given to review the students were asked to find the derivative of arccosh(x)*sqrt(1-x^2).  Maple gives the answer -arccosh(x)*x/sqrt(1-x^2)+sqrt(1-x^2)/(sqrt(x-1)*sqrt(x+1)).   This is the same answer, in a slightly different form, that was given by the test writer. 


Unfortunately, the domain of the function is a single point, x=1 and the expression for the answer does not exist as a real number at any real number.  (Adding  with(RealDomain): does not help.)  The moral is to remember that a user of Maple (or any similar program) is responsible for making sure the answers are sensible when one is not using complex numbers.

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