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

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

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

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

Popular >

derivative of

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

64 (2 + x)^{1}

sin (x^{2} - 5 x)

\frac{d}{d t} (5 - t)

e^{- 0} 0.25 x

\frac{d}{d a} (\frac{( cos ^{2} ( a ) - cos ( a ) )}{sin ( a )})

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