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

The derivative of (x^3/(x+2)) is (2x^3+6x^2)/((x+2)^2)

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

The first derivative of (x^3/(x+2)) is (2x^3+6x^2)/((x+2)^2)

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

\frac{2 x ^{3} + 6 x ^{2}}{( x + 2 ) ^{2}}

Solution steps

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

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

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

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

Simplify

\frac{3 x ^{2} ( x + 2 ) - 1 \cdot x ^{3}}{( x + 2 ) ^{2}} : \frac{2 x ^{3} + 6 x ^{2}}{( x + 2 ) ^{2}}

= \frac{2 x ^{3} + 6 x ^{2}}{( x + 2 ) ^{2}}

x^{9} y^{^{'}} - 9 x^{8} y = 5 y^{2}

\frac{d}{d t} (t - 2 (t - 1) u_{(1)} (t) + (t - 2) u_{(2)} (t) (t))

sin (4 t) cos (3 t)

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

t + 3

What is the derivative of (x^3/(x+2)) ?
The derivative of (x^3/(x+2)) is (2x^3+6x^2)/((x+2)^2)
What is the first derivative of (x^3/(x+2)) ?
The first derivative of (x^3/(x+2)) is (2x^3+6x^2)/((x+2)^2)