Question

how would you differentiate (-(x^2+1)^{1/2))/(1/2)+ln(x+(x^2+1)^(1/2)

Answer 1

If you recognize that ln(x+(x^2+1)^(1/2)) = sinh^-1x, and its derivative is 1/(x^2+1)^(1/2), you will easily obtain the answer:

(1-2x)/(x^2+1)^(1/2)