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

The derivative of ((1-x)x^2)/((1+x^2)) is (-x^4-3x^2+2x)/((1+x^2)^2)

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

The first derivative of ((1-x)x^2)/((1+x^2)) is (-x^4-3x^2+2x)/((1+x^2)^2)

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derivative of

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

\frac{- x ^{4} - 3 x ^{2} + 2 x}{( 1 + x ^{2} ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{( - 3 x ^{2} + 2 x ) ( 1 + x ^{2} ) - 2 x ( 1 - x ) x ^{2}}{( 1 + x ^{2} ) ^{2}} : \frac{- x ^{4} - 3 x ^{2} + 2 x}{( 1 + x ^{2} ) ^{2}}

= \frac{- x ^{4} - 3 x ^{2} + 2 x}{( 1 + x ^{2} ) ^{2}}

What is the derivative of ((1-x)x^2)/((1+x^2)) ?
The derivative of ((1-x)x^2)/((1+x^2)) is (-x^4-3x^2+2x)/((1+x^2)^2)
What is the first derivative of ((1-x)x^2)/((1+x^2)) ?
The first derivative of ((1-x)x^2)/((1+x^2)) is (-x^4-3x^2+2x)/((1+x^2)^2)