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

The derivative of (x^3)/(2-x^2) is (6x^2-x^4)/((2-x^2)^2)

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

The first derivative of (x^3)/(2-x^2) is (6x^2-x^4)/((2-x^2)^2)

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derivative of

\frac{x ^{3}}{2 - x ^{2}}

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

Solution steps

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

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

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

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

Simplify

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

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

(sin^{4} (x))^{^{'}}

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

\frac{d}{d x} (x e^{\frac{y}{x}})

x \to 1 lim ((1 - x)^{2} + 2)

\frac{d}{d x} (\frac{2160}{x ^{2}})

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