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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\frac{d ^{2}}{d x ^{2}} (\frac{7}{8 t ^{6}})

x \to 3 + lim (\frac{x ^{2} - 9}{x - 3})

\frac{x}{5 + x}

\frac{d}{d x} (5 sin (x))

\frac{2 s + 1}{s ^{2} + 1}

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