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}}

\frac{d ^{2}}{d x ^{2}} (\frac{3}{4 x ^{6}})

\int sin (a x) cos (b x) d x

x \to c lim (m x + b)

2 x^{2} - 13 + 1

\int_{0}^{\infty} e^{- 5 t} d t

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)