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

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

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

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

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

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

Solution steps

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

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

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

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

Simplify

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

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

\int 3 x x + 3 d x

\frac{\partial}{\partial v} (sin^{2} (u))

\frac{d}{d x} ((2 x - 3)^{4} (x^{2} + x + 1)^{5})

\int_{0}^{4} \frac{1}{2 x + 1} d x

x \to - \infty lim (9 x^{3})

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