Question

I get everything, but I can't seem to crack this one out, only one I got problems on..

-sqrt[x^2 +1]/x + ln(x + sqrt[x^2 + 1])

Answer 1

for simplicity, let u=sqrt(x^2+1)


-u/x+ ln(x+u)

the derivative is
u/x^2 -1/u du/dx + 1/(x+u) * (1+du/dx)

then, du/dx=1/2 (x^2+1)^-.5 (2x) or
x/sqrt(x^2+1) check me.

Answer 2

I slugged it out the long way without bobpursley's substitution, and got a final of

√(x^2 + 1) / x^2

It would be a horrible mess to type, do you have an answer from the back of the book?