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Popular >

derivative of ln(x/(x-1))

Solution

derivative of

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

integral of tan^3(2x)sec^5(2x)

\int tan^{3} (2 x) sec^{5} (2 x) d x

derivative of e^{2x}cos(4x)

\frac{d}{d x} (e^{2 x} cos (4 x))

integral of 4x(2x^2+1)^7

\int 4 x (2 x^{2} + 1)^{7} d x

integral of 6x^4-5x^3+5x^2+C

\int 6 x^{4} - 5 x^{3} + 5 x^{2} + C d x

(dy)/(dx)=e^{2y-x}

\frac{d y}{d x} = e^{2 y - x}

Frequently Asked Questions (FAQ)

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