giorgiana1976|
College Teacher
|(Level 3) Valedictorian

Posted on

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)` .