What is the derivative of (x^3/((1-x)^2)) ?

The derivative of (x^3/((1-x)^2)) is (x^2(-x+3))/((1-x)^3)

What is the first derivative of (x^3/((1-x)^2)) ?

The first derivative of (x^3/((1-x)^2)) is (x^2(-x+3))/((1-x)^3)

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\frac{d}{d x} (\frac{x ^{3}}{( 1 - x ) ^{2}})

\frac{x ^{2} ( - x + 3 )}{( 1 - x ) ^{3}}

Solution steps

\frac{d}{d x} (\frac{x ^{3}}{( 1 - x ) ^{2}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x ^{3} ) ( 1 - x ) ^{2} - \frac{d}{d x} ( ( 1 - x ) ^{2} ) x ^{3}}{( ( 1 - x ) ^{2} ) ^{2}}

\frac{d}{d x} (x^{3}) = 3 x^{2}

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

= \frac{3 x ^{2} ( 1 - x ) ^{2} - ( - 2 ( 1 - x ) ) x ^{3}}{( ( 1 - x ) ^{2} ) ^{2}}

Simplify

\frac{3 x ^{2} ( 1 - x ) ^{2} - ( - 2 ( 1 - x ) ) x ^{3}}{( ( 1 - x ) ^{2} ) ^{2}} : \frac{x ^{2} ( - x + 3 )}{( 1 - x ) ^{3}}

= \frac{x ^{2} ( - x + 3 )}{( 1 - x ) ^{3}}

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

\int x^{r} d x

\frac{x ^{2} - 6 x + 12}{x - 4}

y^{^{'}} + y = e^{- x} x

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

What is the derivative of (x^3/((1-x)^2)) ?
The derivative of (x^3/((1-x)^2)) is (x^2(-x+3))/((1-x)^3)
What is the first derivative of (x^3/((1-x)^2)) ?
The first derivative of (x^3/((1-x)^2)) is (x^2(-x+3))/((1-x)^3)