What is the derivative of $ln(1+(1/x))$ ?

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Answer 1 · 2015-08-30T15:00:28

$d/dx(ln(1+(1/x))) = (-1)/(x(x+1))$

Although you could use $d/dx (ln(u)) = 1/u (du)/dx$ , the algebra will get messy that way.

Let's rewrite using properties of $ln$ .

$y = ln(1+(1/x)) = ln((x+1)/x)$

$= ln(x+1) - ln(x)$

So

$dy/dx = 1/(x+1) - 1/x = (-1)/(x(x+1))$

What is the derivative of ln(1+(1/x))ln(1+(1/x))?