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

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

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

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

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derivative of

\frac{x ^{3}}{x + 1}

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

Solution steps

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

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

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

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

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

Simplify

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

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

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