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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d x}{d x} = 1

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

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

Simplify

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

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

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