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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

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