Find derivative of (x+1)/(x^2+1)^(1/2)
Use the quotient rule
dy/dx = [ (x^2+1)^(1/2) (1) - (x+1)(1/2)(x^2+1)^(-1/2) (2x) ]/(x^2+1)
= (x^2+1)^(-1/2) [ x^2 + 1 - x(x+1)]/(x^2+1)
= (1-x)/(x^2+1)^(3/2)
or
= (1-x)(x^2+1)^(-3/2)
or
= (1-x)/√(x^2+1)^3