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

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

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

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

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

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

f (x) = 7 (2 - 3 x)^{4}

\int \frac{( x ^{am} - x ^{n} )}{x} d x

y^{^{'}} + 3 y = 2 x e^{- 3 x}

\int 1 1^{x} d x

x \to 0 - lim (\frac{x ^{2}}{5} - \frac{7}{x})

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