Question

Найти дифференциал функции у=(е^х +1) / (е^x - 1)

Answer 1

y=(e^x+1)/(e^x-1)

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

dy/dx=-2e^x/(e^x-1)^2
dy = -2e^xdx/(e^x-1)^2