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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

\frac{d x}{d x} = 1

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

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

Simplify

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

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

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

\int_{0}^{5} 0.2 x d x

n = 1 \sum \infty n (n + 1)

x \to 3 lim (x^{2} - 3 x)

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

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