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

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

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

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

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

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

Solution steps

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

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

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

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

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

Simplify

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

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

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