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

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

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

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

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derivative of

f (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}}

\int_{4}^{x} \frac{( x - 4 ) ^{2}}{72} d x

x \to 1 lim (\frac{x}{x - 1} - \frac{1}{x})

\int \frac{x + 2}{x ^{2} + 4} d x

\frac{\partial}{\partial x} (7 x^{3 y})

\int \frac{x ^{7}}{( 1 + x ^{4} ) ^{2}} d x

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