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

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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

x \to 3 lim (2 x^{2} - 3 x)

\frac{d y}{d x} = 2 x y

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

\int (e^{2 x} + x) d x

- 0.0000272 x^{2} + 0.008459 x + 440

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