What is the derivative of (1-ln(x-1)/((x-1)^2)) ?

The derivative of (1-ln(x-1)/((x-1)^2)) is -(-2ln(x-1)+3)/((x-1)^3)

What is the first derivative of (1-ln(x-1)/((x-1)^2)) ?

The first derivative of (1-ln(x-1)/((x-1)^2)) is -(-2ln(x-1)+3)/((x-1)^3)

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

- \frac{- 2 ln ( x - 1 ) + 3}{( x - 1 ) ^{3}}

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

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

Simplify

\frac{( - \frac{1}{x - 1} ) ( x - 1 ) ^{2} - 2 ( x - 1 ) ( 1 - ln ( x - 1 ) )}{( ( x - 1 ) ^{2} ) ^{2}} : - \frac{- 2 ln ( x - 1 ) + 3}{( x - 1 ) ^{3}}

= - \frac{- 2 ln ( x - 1 ) + 3}{( x - 1 ) ^{3}}

\frac{d}{d x} (\frac{1}{x ^{\frac{3}{2}}})

\frac{1 - 4 t}{5 + t}

\frac{3 s}{s ^{2} + 4}

x + 6 y = 8, x + 8 = y^{2}

\frac{d}{d x} (- \frac{y}{x + 2 y})

What is the derivative of (1-ln(x-1)/((x-1)^2)) ?
The derivative of (1-ln(x-1)/((x-1)^2)) is -(-2ln(x-1)+3)/((x-1)^3)
What is the first derivative of (1-ln(x-1)/((x-1)^2)) ?
The first derivative of (1-ln(x-1)/((x-1)^2)) is -(-2ln(x-1)+3)/((x-1)^3)