What is the derivative of (sqrt(x)-1)/(x-1) ?

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

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

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

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derivative of

\frac{x - 1}{x - 1}

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

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3 x^{- 3} (x^{4} - 3 x^{3} + 10 x - 9)

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\int \frac{9 e ^{x}}{e ^{x} - 1} d x

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