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

The derivative of ln(1+1/x) is -1/(x(x+1))

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

The first derivative of ln(1+1/x) is -1/(x(x+1))

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derivative of

ln (1 + \frac{1}{x})

- \frac{1}{x ( x + 1 )}

Solution steps

\frac{d}{d x} (ln (1 + \frac{1}{x}))

Apply the chain rule:

\frac{1}{1 + \frac{1}{x}} \frac{d}{d x} (1 + \frac{1}{x})

= \frac{1}{1 + \frac{1}{x}} \frac{d}{d x} (1 + \frac{1}{x})

\frac{d}{d x} (1 + \frac{1}{x}) = - \frac{1}{x ^{2}}

= \frac{1}{1 + \frac{1}{x}} (- \frac{1}{x ^{2}})

Simplify

\frac{1}{1 + \frac{1}{x}} (- \frac{1}{x ^{2}}) : - \frac{1}{x ( x + 1 )}

= - \frac{1}{x ( x + 1 )}

\frac{d y}{d x} = \frac{( x ^{3} - 2 y )}{x}

5 x^{3} + 2 x + 4, at x = 1

\int \frac{2}{9 - x ^{2}} d x

f (x) = x^{2} sin (4 x^{2})

\frac{\partial}{\partial x} (2 z)

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