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

The derivative of 2/(2x-1-1/x) is (-4x+1)/(x^2(2x-1)^2)

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

The first derivative of 2/(2x-1-1/x) is (-4x+1)/(x^2(2x-1)^2)

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

\frac{- 4 x + 1}{x ^{2} ( 2 x - 1 ) ^{2}}

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{d}{d x} (\frac{2}{2 x - 1}) = - \frac{4}{( 2 x - 1 ) ^{2}}

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

= - \frac{4}{( 2 x - 1 ) ^{2}} - (- \frac{1}{x ^{2}})

Simplify

- \frac{4}{( 2 x - 1 ) ^{2}} - (- \frac{1}{x ^{2}}) : \frac{- 4 x + 1}{x ^{2} ( 2 x - 1 ) ^{2}}

= \frac{- 4 x + 1}{x ^{2} ( 2 x - 1 ) ^{2}}

\int \frac{5 x - 3}{x ( x - 3 ) ( x + 1 )} d x

\int x cos (7 π x^{2}) d x

- (y + t) = \frac{d y}{d t}

\int 3^{5 x} d x

3 y^{^{''}} + 10 y^{^{'}} = 0

What is the derivative of 2/(2x-1-1/x) ?
The derivative of 2/(2x-1-1/x) is (-4x+1)/(x^2(2x-1)^2)
What is the first derivative of 2/(2x-1-1/x) ?
The first derivative of 2/(2x-1-1/x) is (-4x+1)/(x^2(2x-1)^2)