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

The derivative of (x^3)/(1-x^2) is (3x^2-x^4)/((1-x^2)^2)

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

The first derivative of (x^3)/(1-x^2) is (3x^2-x^4)/((1-x^2)^2)

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derivative of

\frac{x ^{3}}{1 - x ^{2}}

\frac{3 x ^{2} - x ^{4}}{( 1 - x ^{2} ) ^{2}}

Solution steps

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

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

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

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

Simplify

\frac{3 x ^{2} ( 1 - x ^{2} ) - ( - 2 x ) x ^{3}}{( 1 - x ^{2} ) ^{2}} : \frac{3 x ^{2} - x ^{4}}{( 1 - x ^{2} ) ^{2}}

= \frac{3 x ^{2} - x ^{4}}{( 1 - x ^{2} ) ^{2}}

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

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

f (x) = x sin (x), 0, 2 π

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

f (x) = x - 5

What is the derivative of (x^3)/(1-x^2) ?
The derivative of (x^3)/(1-x^2) is (3x^2-x^4)/((1-x^2)^2)
What is the first derivative of (x^3)/(1-x^2) ?
The first derivative of (x^3)/(1-x^2) is (3x^2-x^4)/((1-x^2)^2)