Question

Find the dy/dx
Please

Answer 1

Explanation:

Given that,

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

We need to find dy/dx

`(dy)/(dx)=(d)/(dx)((e^x+1)/(1-e^x))\\\\=(1-e^x(d)/(dx)(e^x+1)-(e^x+1)(d)/(dx)(1-e^x)))/((1-e^x)^2)\\\\\because (d(e^x))/(dx)=e^x\\\\=(1-e^x(e^x)-(e^x+1)(-e^x))/((1-e^x)^2)\\\\=(e^x(e^x+1)+(1-e^x)e^x)/((1-e^x)^2)\\\\=\frac{\mathrm{e}^x\left(\mathrm{e}^x+1\right)+\left(1-\mathrm{e}^x\right)\mathrm{e}^x}{\left(1-\mathrm{e}^x\right)^2}\\\\=\frac{2\mathrm{e}^x}{\left(\mathrm{e}^x-1\right)^2}`

Hence, this is the required solution.