What is the derivative of x/(1-\frac{1){x^2}} ?

The derivative of x/(1-\frac{1){x^2}} is (x^2(x^2-3))/((x^2-1)^2)

What is the first derivative of x/(1-\frac{1){x^2}} ?

The first derivative of x/(1-\frac{1){x^2}} is (x^2(x^2-3))/((x^2-1)^2)

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derivative of

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

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

Solution steps

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

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

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

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

Simplify

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

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

What is the derivative of x/(1-\frac{1){x^2}} ?
The derivative of x/(1-\frac{1){x^2}} is (x^2(x^2-3))/((x^2-1)^2)
What is the first derivative of x/(1-\frac{1){x^2}} ?
The first derivative of x/(1-\frac{1){x^2}} is (x^2(x^2-3))/((x^2-1)^2)