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

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

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

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

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

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

Solution steps

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

Simplify

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

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

\int \frac{x ^{3}}{3} + x d x

\int cos (3 z + 4) d z

n = 1 \sum \infty \frac{1}{n 2 ^{n}}

\frac{d y}{d x} = 12 x^{11} y

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

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