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

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

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

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

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

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Simplify

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

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

e^{x}

\int \frac{2 x ^{3} - 6 x ^{2} - 10 x - 6}{x ^{2} - 1} d x

3 y^{^{''}} - y^{^{'}} + 2 y = 0, y (0) = 2, y^{^{'}} (0) = 0

\int \frac{tan ^{3} ( \frac{4}{z} )}{z ^{2}} d z

\int \frac{1}{e ^{\frac{x}{2}}} d x

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