Find the derivative of `y=ln((1+e^x)/(1-e^x)) ` :
Use a property of the natural logarithm to rewrite as:
`y=ln(1+e^x)-ln(1-e^x) `
If u is a differentiable function of x, then ` d/(dx)ln(u)=(du)/u ` so
`(dy)/(dx)=e^x/(1+e^x)-(-e^x)/(1-e^x)`
Subtracting the fractions we get:
`(dy)/(dx)=(e^x(1-e^x)-(-e^x)(1+e^x))/((1+e^x)(1-e^x)) `
Clearing the parantheses and adding like terms we get:
`(dy)/(dx)=(2e^x)/(1-e^(2x)) `
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