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

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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

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