What is derivative of f(x)=ln(e^x-2) ?

We notice that the function f(x) is a result of composition of two
functions, therefore we'll apply the chain rule to find out the derivative of
f(x).

f(x) = u(v(x))=>f'(x) = derivative of outside
function*inside function*derivative of inside
function.

Let outside function be u and inside function
be v.

f'(x) = [ln(` e^x - 2` )]'*(` e^x - 2` )'=>f'(x) =
[1/(` e^x - 2` )]*(`e^x` )


Therefore, the
requested derivative of the given function is f'(x) = `e^x/(e^x - 2)`
.