What is the derivative of (sqrt(x-1)/(2x-3)) ?

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

What is the first derivative of (sqrt(x-1)/(2x-3)) ?

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

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