Differentiate: ln((e^x+1)/e^x-1))

Chain rule: First resolve the log differential, then resolve the fraction integration either by knowing the formula for it or by writing (e^x+1)/(e^x-1) as (e^x+1)(e^x-1)^(-1) and applying chain rule againLet’s assume that the formula for the fraction differential is not known
dy/dx= (e^x-1)/(e^x+1) * (e^x*(e^x-1)^(-1)-e^x*(e*x+1)(e^x-1)^(-2))
After the differential has been resolved further simplification can be obtained by putting the same denominator in the large brackets and then realising that some of it can be simplified with the first fraction of the equation
dy/dx= (e^x-1)/(e^x+1) * (e^2x-2e^x-e^2x)/(e^x-1)^2)dy/dx= (-2e^x)/(e^2x-1)