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

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

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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)` .

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