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

The derivative of f(x)=(x^3)/(x^2+2) is (x^4+6x^2)/((x^2+2)^2)

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

The first derivative of f(x)=(x^3)/(x^2+2) is (x^4+6x^2)/((x^2+2)^2)

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derivative of

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

\frac{x ^{4} + 6 x ^{2}}{( x ^{2} + 2 ) ^{2}}

Solution steps

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

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

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

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

Simplify

\frac{3 x ^{2} ( x ^{2} + 2 ) - 2 x x ^{3}}{( x ^{2} + 2 ) ^{2}} : \frac{x ^{4} + 6 x ^{2}}{( x ^{2} + 2 ) ^{2}}

= \frac{x ^{4} + 6 x ^{2}}{( x ^{2} + 2 ) ^{2}}

(- 2, - 8), (3, 2)

(5.5) (4.2)

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

\frac{d}{d x} (\frac{x}{x ^{2} + 7})

sin (k t)

What is the derivative of f(x)=(x^3)/(x^2+2) ?
The derivative of f(x)=(x^3)/(x^2+2) is (x^4+6x^2)/((x^2+2)^2)
What is the first derivative of f(x)=(x^3)/(x^2+2) ?
The first derivative of f(x)=(x^3)/(x^2+2) is (x^4+6x^2)/((x^2+2)^2)