can anyone just double check these for me please??

differentiation

ln (radical((x^2) +4)) = x / (x^2) + 4

ln (5-x)^6 = -6/(5^-x)

ln ( x * (e^x) ) = (e^-x)((e^x)x + e^x )) / x

ln (e^x) / radical(e^x) + 1 = 1 / (radical(e^x) + 1) - radical(e^x) log (e^x) / 2(radical(e^x) +1)^2