f(x)=ln(e^x-e^-x), x>0

Question

By applying in turn the Composite and Quotient Rules, find derivative and second derivative.

Thanks.

Answer 1

f '(x) = (e^x + e^-x)/(e^x - e^-x)
= e^-x(e^(2x) + 1)/(e^-x(e^(2x) - 1)
= (e^(2x) + 1)/(e^(2x) -1)

now use the quotient rule to get the second derivative,
let me know what you got.